It really doesnt matter the new owner IS responsible your your deposits, if he didnt get them thats HIS fault not yours.
As long as you have a recipet and lease stating you paid, the old landlord is usually NOT liable to YOU for the deposit, since the closing is supposed to be a Finality.
And if the landlord doesnt turn over the deposits its usually deducted from the escrow account, or they agree to lower the sales price.
So you will have a claim against the new owner for the $650
OH DO YOU HAVE A LEASE?
If you send the letter and dont have a lease...... then expect a 30 day notice next month.. and your defense in NOT paying next months rent is you have a notice (you have a copy right?)....that there was no security deposit transferred in the sale.
The new landlord cannot charge you a second deposit...., but CAN charge you another deposit for say the second months security, or last months rent, and it must be stated in the new lease.