All functions in the API-MS-Win-Core-LibraryLoader-L1-1-0 set are documented exports from KERNEL32 or USER32:

The implementations in KERNEL32 version 6.1 and higher are just stubs which transfer the handling to wherever the schema redirects the API Set.

The two USER32 functions, LoadStringA and LoadStringW, continue to have non-trivial implementations that are exported from USER32 version 6.1 and higher. Since version 6.0 however, those implementations reinterpret in terms of the undocumented KERNEL32 function LoadStringBaseExW. This too is implemented only as a stub in version 6.1 and higher, transferring explicitly to KERNELBASE.

New Locations

Non-trivial implementations of all functions in this API Set are exported from KERNELBASE version 6.1 and higher.

Schema Redirection

The Windows 7 schema redirects this API Set to KERNELBASE. Thus: