> This worries me because my mother, who currently resides in a SE Asian nation, is transferring some of her money to me (in the hope that she can use it when she migrates to the US).

The problem is what you are describing is not exactly legal. You are acting as a money transmitter for your mother; and this might even trigger for you some complex tax obligations.

What you should do is open a Chase bank account for your mother. You already bank with the agency.