diff --git a/llvm/lib/IR/Constants.cpp b/llvm/lib/IR/Constants.cpp
--- a/llvm/lib/IR/Constants.cpp
+++ b/llvm/lib/IR/Constants.cpp
@@ -1914,6 +1914,12 @@
   getContext().pImpl->DSOLocalEquivalents.erase(getGlobalValue());
   NewEquiv = this;
   setOperand(0, Func);
+
+  if (Func->getType() != getType()) {
+    // It is ok to mutate the type here because this constant should always
+    // reflect the type of the function it's holding.
+    mutateType(Func->getType());
+  }
   return nullptr;
 }
 
diff --git a/llvm/lib/Transforms/Utils/ValueMapper.cpp b/llvm/lib/Transforms/Utils/ValueMapper.cpp
--- a/llvm/lib/Transforms/Utils/ValueMapper.cpp
+++ b/llvm/lib/Transforms/Utils/ValueMapper.cpp
@@ -432,6 +432,20 @@
   if (BlockAddress *BA = dyn_cast<BlockAddress>(C))
     return mapBlockAddress(*BA);
 
+  if (const auto *E = dyn_cast<DSOLocalEquivalent>(C)) {
+    auto *Val = mapValue(E->getGlobalValue());
+    GlobalValue *GV = dyn_cast<GlobalValue>(Val);
+    if (GV)
+      return getVM()[E] = DSOLocalEquivalent::get(GV);
+
+    auto *Func = cast<Function>(Val->stripPointerCastsAndAliases());
+    Type *NewTy = E->getType();
+    if (TypeMapper)
+      NewTy = TypeMapper->remapType(NewTy);
+    return getVM()[E] = llvm::ConstantExpr::getBitCast(
+               DSOLocalEquivalent::get(Func), NewTy);
+  }
+
   auto mapValueOrNull = [this](Value *V) {
     auto Mapped = mapValue(V);
     assert((Mapped || (Flags & RF_NullMapMissingGlobalValues)) &&
diff --git a/llvm/test/Linker/DSOLocalEquivalent.ll b/llvm/test/Linker/DSOLocalEquivalent.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Linker/DSOLocalEquivalent.ll
@@ -0,0 +1,34 @@
+; RUN: llvm-link %s %S/Inputs/DSOLocalEquivalent.ll -S | FileCheck %s
+; RUN: llvm-link %S/Inputs/DSOLocalEquivalent.ll %s -S | FileCheck %s
+
+declare void @extern_func()
+declare void @defined_extern_func()
+declare hidden void @hidden_func()
+
+; CHECK:      define void @call_extern_func() {
+; CHECK-NEXT:   call void dso_local_equivalent @extern_func()
+; CHECK-NEXT:   ret void
+; CHECK-NEXT: }
+define void @call_extern_func() {
+
+  call void dso_local_equivalent @extern_func()
+  ret void
+}
+
+; CHECK:      define void @call_defined_extern_func() {
+; CHECK-NEXT:   call void dso_local_equivalent @defined_extern_func()
+; CHECK-NEXT:   ret void
+; CHECK-NEXT: }
+define void @call_defined_extern_func() {
+  call void dso_local_equivalent @defined_extern_func()
+  ret void
+}
+
+; CHECK:      define void @call_hidden_func() {
+; CHECK-NEXT:   call void dso_local_equivalent @hidden_func()
+; CHECK-NEXT:   ret void
+; CHECK-NEXT: }
+define void @call_hidden_func() {
+  call void dso_local_equivalent @hidden_func()
+  ret void
+}
diff --git a/llvm/test/Linker/Inputs/DSOLocalEquivalent.ll b/llvm/test/Linker/Inputs/DSOLocalEquivalent.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Linker/Inputs/DSOLocalEquivalent.ll
@@ -0,0 +1,7 @@
+define void @defined_extern_func() {
+  ret void
+}
+
+define hidden void @hidden_func() {
+  ret void
+}
diff --git a/llvm/test/ThinLTO/X86/DSOLocalEquivalent.ll b/llvm/test/ThinLTO/X86/DSOLocalEquivalent.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/ThinLTO/X86/DSOLocalEquivalent.ll
@@ -0,0 +1,17 @@
+; RUN: llvm-as %s -o %t1.bc
+; RUN: llvm-lto2 run %t1.bc -o %t2.o -r=%t1.bc,caller,plx -r=%t1.bc,extern_func,plx -save-temps
+; RUN: llvm-dis %t2.o.0.5.precodegen.bc -o - | FileCheck %s
+
+target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-f80:128-n8:16:32:64-S128"
+target triple = "x86_64-unknown-fuchsia"
+
+declare void @extern_func()
+
+; CHECK:      define {{.*}} void @caller() {{.*}}{
+; CHECK-NEXT:   tail call void dso_local_equivalent @extern_func()
+; CHECK-NEXT:   ret void
+; CHECK-NEXT: }
+define void @caller() {
+  call void dso_local_equivalent @extern_func()
+  ret void
+}