How to move the payments to the accounts?

Any Fee that is collected goes to Undeposited Funds. You would then go to Income -> Deposit Payment screen -> Select the account you want to deposit to -> Add the payments you want to deposit and save.

In cases like bank deposits, you can deposit those fee payments only when the deposit is verified and hits the bank. In cases of any cheque payment, you can again deposit to the appropriate bank when cleared.

 So any income received is parked in Undeposited Funds and can be deposit to the bank account on the actual dates.

This screen is also used for cash collections, all income would go to Undeposited Funds and end of day, the cash can be tallied to match the system total shown in Deposit Payment screen and deposited to the appropriate accounts.

This method mentioned solves the problem and also streamlines the activities, segregate income and handle deposit by transaction/payment type/date easilt and minimises any possible errors.