I honestly have no idea what you're talking about unless you're meaning about immigrating with more than 10,000€ worth of physical currency? I went through immigrating to EU recently and the declaration was as simple as signing a statement that I am able to show records of how I got the money if required by the country I was moving to, and one of the examples was as simple as bank statements showing you had an income that supported you having such money.

I don't think you're talking about this, so maybe you can link to a government site with the relevant law you're discussing? It's pretty trivial to demonstrate it in most cases, and I think even a paper ledger is enough for most situations.