diff --git a/llvm/test/tools/sycl-post-link/sym_but_no_split.ll b/llvm/test/tools/sycl-post-link/sym_but_no_split.ll
new file mode 100644
index 0000000000000..ec2050ad8775a
--- /dev/null
+++ b/llvm/test/tools/sycl-post-link/sym_but_no_split.ll
@@ -0,0 +1,25 @@
+; This test checks that the post-link tool produces a correct resulting file
+; table and a symbol file for an input module with two kernels when no code
+; splitting is requested.
+;
+; RUN: sycl-post-link -symbols -spec-const=rt -S %s -o %t.files.table
+; RUN: FileCheck %s -input-file=%t.files.table --check-prefixes CHECK-TABLE
+; RUN: FileCheck %s -input-file=%t.files_0.sym --match-full-lines --check-prefixes CHECK-SYM
+
+define dso_local spir_kernel void @KERNEL_AAA() {
+; CHECK-SYM-NOT: {{[a-zA-Z0-9._@]+}}
+; CHECK-SYM: KERNEL_AAA
+entry:
+  ret void
+}
+
+define dso_local spir_kernel void @KERNEL_BBB() {
+; CHECK-SYM-NEXT: KERNEL_BBB
+; CHECK-SYM-EMPTY:
+entry:
+  ret void
+}
+
+; CHECK-TABLE: [Code|Properties|Symbols]
+; CHECK-TABLE-NEXT: {{.*}}files_0.sym
+; CHECK-TABLE-EMPTY:
diff --git a/llvm/tools/sycl-post-link/sycl-post-link.cpp b/llvm/tools/sycl-post-link/sycl-post-link.cpp
index 39d21018f7644..2d1d01ce7801a 100644
--- a/llvm/tools/sycl-post-link/sycl-post-link.cpp
+++ b/llvm/tools/sycl-post-link/sycl-post-link.cpp
@@ -121,23 +121,51 @@ static void writeToFile(std::string Filename, std::string Content) {
   OS.close();
 }
 
-// Output parameter ResKernelModuleMap is a map containing groups of kernels
-// with same values of the sycl-module-id attribute.
-// The function fills ResKernelModuleMap using input module M.
+// Describes scope covered by each entry in the module-kernel map populated by
+// the collectKernelModuleMap function.
+enum KernelMapEntryScope {
+  Scope_PerKernel, // one entry per kernel
+  Scope_PerModule, // one entry per module
+  Scope_Global     // single entry in the map for all kernels
+};
+
+// This function decides how kernels of the input module M will be distributed
+// ("split") into multiple modules based on the command options and IR
+// attributes. The decision is recorded in the output map parameter
+// ResKernelModuleMap which maps some key to a group of kernels. Each such group
+// along with IR it depends on (globals, functions from its call graph,...) will
+// constitute a separate module.
 static void collectKernelModuleMap(
     Module &M, std::map<StringRef, std::vector<Function *>> &ResKernelModuleMap,
-    bool OneKernelPerModule) {
-
-  constexpr char ATTR_SYCL_MODULE_ID[] = "sycl-module-id";
+    KernelMapEntryScope EntryScope) {
 
   for (auto &F : M.functions()) {
     if (F.getCallingConv() == CallingConv::SPIR_KERNEL) {
-      if (OneKernelPerModule) {
+      switch (EntryScope) {
+      case Scope_PerKernel:
         ResKernelModuleMap[F.getName()].push_back(&F);
-      } else if (F.hasFnAttribute(ATTR_SYCL_MODULE_ID)) {
+        break;
+      case Scope_PerModule: {
+        constexpr char ATTR_SYCL_MODULE_ID[] = "sycl-module-id";
+
+        // TODO It may make sense to group all kernels w/o the attribute into
+        // a separate module rather than issuing an error. Should probably be
+        // controlled by an option.
+        if (!F.hasFnAttribute(ATTR_SYCL_MODULE_ID))
+          error("no '" + Twine(ATTR_SYCL_MODULE_ID) +
+                "' attribute in kernel '" + F.getName() +
+                "', per-module split not possible");
         Attribute Id = F.getFnAttribute(ATTR_SYCL_MODULE_ID);
         StringRef Val = Id.getValueAsString();
         ResKernelModuleMap[Val].push_back(&F);
+        break;
+      }
+      case Scope_Global:
+        // the map key is not significant here
+        ResKernelModuleMap["<GLOBAL>"].push_back(&F);
+        break;
+      default:
+        llvm_unreachable("unknown scope");
       }
     }
   }
@@ -375,8 +403,12 @@ int main(int argc, char **argv) {
 
   std::map<StringRef, std::vector<Function *>> GlobalsSet;
 
-  if (DoSplit || DoSymGen)
-    collectKernelModuleMap(*MPtr, GlobalsSet, SplitMode == SPLIT_PER_KERNEL);
+  if (DoSplit || DoSymGen) {
+    KernelMapEntryScope Scope = Scope_Global;
+    if (DoSplit)
+      Scope = SplitMode == SPLIT_PER_KERNEL ? Scope_PerKernel : Scope_PerModule;
+    collectKernelModuleMap(*MPtr, GlobalsSet, Scope);
+  }
 
   std::vector<std::unique_ptr<Module>> ResultModules;
   std::vector<SpecIDMapTy> ResultSpecIDMaps;