Executing MiniDumpWriteDump within the specific process provides healthy dump file.
Executing MiniDumpWriteDump from external process, where hProcess an
Ok.. found the solution for that..
The external process project was build for "AnyCPU" platform (and as it doesn't execute only-64 bit commands, it was running for 32-bit). Setting it to x64 made it possible to dump another 64 bit process.
And I would recommend to anyone who encounter this issue, to create separated projects, one for 32 bit and one for 64 bit.