If you had previously requested a change of address with USPS and you decide to close your Anytime Mailbox account, then you should also cancel the change of address request with USPS.
However, if you did not request a change of address with USPS, then you only need to contact your senders and inform them of your new address.
It is important to note that the USPS Form 1583 is not a change of address form.