The answer is no.
A LEGITIMATE Remington Rand without an inspector's stamp or US Property mark would be highly unusual. For it to lack those but have the P would be extremely highly unusual. So unusual that it would be the seller's responsibility to say just how it came about and to document it, if he wants a big price for it.
Don't you and your brother go into this pre-sold on a tall story. I don't have to prove anything, you and he don't have to prove anything, it is up to the guy trying to put it off on you to prove one of the very very small ways for such a gun to exist.
I must ask, does it even have a serial number?