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
@@ -1908,6 +1908,12 @@
   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
@@ -412,6 +412,20 @@
   if (BlockAddress *BA = dyn_cast<BlockAddress>(C))
     return mapBlockAddress(*BA);
 
+  if (const auto *Equiv = dyn_cast<DSOLocalEquivalent>(C)) {
+    auto *Val = mapValue(Equiv->getGlobalValue());
+    GlobalValue *GV = dyn_cast<GlobalValue>(Val);
+    if (GV)
+      return getVM()[Equiv] = DSOLocalEquivalent::get(GV);
+
+    auto *Func = cast<Function>(Val->stripPointerCastsAndAliases());
+    Type *NewTy = Equiv->getType();
+    if (TypeMapper)
+      NewTy = TypeMapper->remapType(NewTy);
+    return getVM()[Equiv] = llvm::ConstantExpr::getBitCast(
+               DSOLocalEquivalent::get(Func), NewTy);
+  }
+
   auto mapValueOrNull = [this](Value *V) {
     auto Mapped = mapValue(V);
     assert((Mapped || (Flags & RF_NullMapMissingGlobalValues)) &&