diff --git a/src/compiler/checker.ts b/src/compiler/checker.ts
index fcb93c45dc1dd..c10bec95be42d 100644
--- a/src/compiler/checker.ts
+++ b/src/compiler/checker.ts
@@ -23003,6 +23003,24 @@ export function createTypeChecker(host: TypeCheckerHost): TypeChecker {
                         }
                     }
                 }
+                if (sourceFlags & TypeFlags.TemplateLiteral) {
+                    if (arrayIsEqualTo((source as TemplateLiteralType).texts, (target as TemplateLiteralType).texts)) {
+                        const sourceTypes = (source as TemplateLiteralType).types;
+                        const targetTypes = (target as TemplateLiteralType).types;
+                        result = Ternary.True;
+                        for (let i = 0; i < sourceTypes.length; i++) {
+                            if (!(result &= isRelatedTo(sourceTypes[i], targetTypes[i], RecursionFlags.Both, /*reportErrors*/ false))) {
+                                break;
+                            }
+                        }
+                        return result;
+                    }
+                }
+                if (sourceFlags & TypeFlags.StringMapping) {
+                    if ((source as StringMappingType).symbol === (target as StringMappingType).symbol) {
+                        return isRelatedTo((source as StringMappingType).type, (target as StringMappingType).type, RecursionFlags.Both, /*reportErrors*/ false);
+                    }
+                }
                 if (!(sourceFlags & TypeFlags.Object)) {
                     return Ternary.False;
                 }
diff --git a/tests/baselines/reference/assignmentToConditionalBrandedStringTemplateOrMapping.js b/tests/baselines/reference/assignmentToConditionalBrandedStringTemplateOrMapping.js
new file mode 100644
index 0000000000000..4e6244df8e0e1
--- /dev/null
+++ b/tests/baselines/reference/assignmentToConditionalBrandedStringTemplateOrMapping.js
@@ -0,0 +1,21 @@
+//// [tests/cases/compiler/assignmentToConditionalBrandedStringTemplateOrMapping.ts] ////
+
+//// [assignmentToConditionalBrandedStringTemplateOrMapping.ts]
+let a: (<T>() => T extends `${'a' & { a: 1 }}` ? 1 : 2) = null!;
+let b: (<T>() => T extends `${'a' & { a: 1 }}` ? 1 : 2) = null!;
+
+a = b;
+
+let c: (<T>() => T extends Uppercase<'a' & { a: 1 }> ? 1 : 2) = null!;
+let d: (<T>() => T extends Uppercase<'a' & { a: 1 }> ? 1 : 2) = null!;
+
+c = d;
+
+
+//// [assignmentToConditionalBrandedStringTemplateOrMapping.js]
+var a = null;
+var b = null;
+a = b;
+var c = null;
+var d = null;
+c = d;
diff --git a/tests/baselines/reference/assignmentToConditionalBrandedStringTemplateOrMapping.symbols b/tests/baselines/reference/assignmentToConditionalBrandedStringTemplateOrMapping.symbols
new file mode 100644
index 0000000000000..250742a4b1986
--- /dev/null
+++ b/tests/baselines/reference/assignmentToConditionalBrandedStringTemplateOrMapping.symbols
@@ -0,0 +1,37 @@
+//// [tests/cases/compiler/assignmentToConditionalBrandedStringTemplateOrMapping.ts] ////
+
+=== assignmentToConditionalBrandedStringTemplateOrMapping.ts ===
+let a: (<T>() => T extends `${'a' & { a: 1 }}` ? 1 : 2) = null!;
+>a : Symbol(a, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 0, 3))
+>T : Symbol(T, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 0, 9))
+>T : Symbol(T, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 0, 9))
+>a : Symbol(a, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 0, 37))
+
+let b: (<T>() => T extends `${'a' & { a: 1 }}` ? 1 : 2) = null!;
+>b : Symbol(b, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 1, 3))
+>T : Symbol(T, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 1, 9))
+>T : Symbol(T, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 1, 9))
+>a : Symbol(a, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 1, 37))
+
+a = b;
+>a : Symbol(a, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 0, 3))
+>b : Symbol(b, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 1, 3))
+
+let c: (<T>() => T extends Uppercase<'a' & { a: 1 }> ? 1 : 2) = null!;
+>c : Symbol(c, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 5, 3))
+>T : Symbol(T, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 5, 9))
+>T : Symbol(T, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 5, 9))
+>Uppercase : Symbol(Uppercase, Decl(lib.es5.d.ts, --, --))
+>a : Symbol(a, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 5, 44))
+
+let d: (<T>() => T extends Uppercase<'a' & { a: 1 }> ? 1 : 2) = null!;
+>d : Symbol(d, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 6, 3))
+>T : Symbol(T, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 6, 9))
+>T : Symbol(T, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 6, 9))
+>Uppercase : Symbol(Uppercase, Decl(lib.es5.d.ts, --, --))
+>a : Symbol(a, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 6, 44))
+
+c = d;
+>c : Symbol(c, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 5, 3))
+>d : Symbol(d, Decl(assignmentToConditionalBrandedStringTemplateOrMapping.ts, 6, 3))
+
diff --git a/tests/baselines/reference/assignmentToConditionalBrandedStringTemplateOrMapping.types b/tests/baselines/reference/assignmentToConditionalBrandedStringTemplateOrMapping.types
new file mode 100644
index 0000000000000..61dc9b88001e7
--- /dev/null
+++ b/tests/baselines/reference/assignmentToConditionalBrandedStringTemplateOrMapping.types
@@ -0,0 +1,51 @@
+//// [tests/cases/compiler/assignmentToConditionalBrandedStringTemplateOrMapping.ts] ////
+
+=== assignmentToConditionalBrandedStringTemplateOrMapping.ts ===
+let a: (<T>() => T extends `${'a' & { a: 1 }}` ? 1 : 2) = null!;
+>a : <T>() => T extends `${"a" & { a: 1; }}` ? 1 : 2
+>  : ^ ^^^^^^^                                      
+>a : 1
+>  : ^
+>null! : null
+>      : ^^^^
+
+let b: (<T>() => T extends `${'a' & { a: 1 }}` ? 1 : 2) = null!;
+>b : <T>() => T extends `${"a" & { a: 1; }}` ? 1 : 2
+>  : ^ ^^^^^^^                                      
+>a : 1
+>  : ^
+>null! : null
+>      : ^^^^
+
+a = b;
+>a = b : <T>() => T extends `${"a" & { a: 1; }}` ? 1 : 2
+>      : ^ ^^^^^^^                                      
+>a : <T>() => T extends `${"a" & { a: 1; }}` ? 1 : 2
+>  : ^ ^^^^^^^                                      
+>b : <T>() => T extends `${"a" & { a: 1; }}` ? 1 : 2
+>  : ^ ^^^^^^^                                      
+
+let c: (<T>() => T extends Uppercase<'a' & { a: 1 }> ? 1 : 2) = null!;
+>c : <T>() => T extends Uppercase<"a" & { a: 1; }> ? 1 : 2
+>  : ^ ^^^^^^^                                            
+>a : 1
+>  : ^
+>null! : null
+>      : ^^^^
+
+let d: (<T>() => T extends Uppercase<'a' & { a: 1 }> ? 1 : 2) = null!;
+>d : <T>() => T extends Uppercase<"a" & { a: 1; }> ? 1 : 2
+>  : ^ ^^^^^^^                                            
+>a : 1
+>  : ^
+>null! : null
+>      : ^^^^
+
+c = d;
+>c = d : <T>() => T extends Uppercase<"a" & { a: 1; }> ? 1 : 2
+>      : ^ ^^^^^^^                                            
+>c : <T>() => T extends Uppercase<"a" & { a: 1; }> ? 1 : 2
+>  : ^ ^^^^^^^                                            
+>d : <T>() => T extends Uppercase<"a" & { a: 1; }> ? 1 : 2
+>  : ^ ^^^^^^^                                            
+
diff --git a/tests/cases/compiler/assignmentToConditionalBrandedStringTemplateOrMapping.ts b/tests/cases/compiler/assignmentToConditionalBrandedStringTemplateOrMapping.ts
new file mode 100644
index 0000000000000..475e42e2f138b
--- /dev/null
+++ b/tests/cases/compiler/assignmentToConditionalBrandedStringTemplateOrMapping.ts
@@ -0,0 +1,9 @@
+let a: (<T>() => T extends `${'a' & { a: 1 }}` ? 1 : 2) = null!;
+let b: (<T>() => T extends `${'a' & { a: 1 }}` ? 1 : 2) = null!;
+
+a = b;
+
+let c: (<T>() => T extends Uppercase<'a' & { a: 1 }> ? 1 : 2) = null!;
+let d: (<T>() => T extends Uppercase<'a' & { a: 1 }> ? 1 : 2) = null!;
+
+c = d;