The link you reference refers to gift tax, which is filed by the payee, not the recipient. There is no actual tax paid, it is simply using up the estate tax exclusion for any amounts over 11K per person, per year. If the grandmother were a US citizen, she would file the paperwork, not him. I don’t see where this addresses a foreigner (non-US taxpayer) making a gift to a citizen.
Note: Moving $250K across borders via wire transfer or otherwise, will likely be monitored by the feds. It is likely to raise flags as potential money laundering.
I think this issue is best handled by a legal professional, not a message board.