Im not sure of theres another way to transfer money, but I havent come across any. So if there is then disregard this.
So say you have an account with some money, but you want to start a new account.
You arent going to want to regain all of that cash.
All you have to do:
1. Put an item up for sale(On the new account) for however much you want to transfer.
2. Switch accounts to the one with the money.
3. On the main account, buy the item from the Item Trader.
4. Just send the item back in a letter
5. Log back into the new account and you've got the money and your item back.
Huzzah!
(I dont think you can just mail money, can you?)
Hope this helps, and if theres an wasier way, then this is useless