Is she accessing the e-mail using AOL's web interface or via an e-mail client such as Outlook, Thunderbird, etc.?
Presuming the web interface is being used: As far as I am aware the transfer of contacts is easy using any e-mail service's "export" function for contacts then importing them on the service where one wants them loaded. There are scads of tutorials on the web about precisely how each of these things are done for virtually any e-mail provider you can name. It is also a cinch to forward any future incoming e-mail to another account. Getting existing e-mail messages over is a bit more involved, and I'd do a web search on something like "AOL transfer existing inbox to Gmail" or similar. My first instinct would be to forward all of the existing inbox messages in groups and, as soon as I'd verified they've arrived, deleting them from the AOL side. There may be something easier.
Forwarding occurs very quickly, often seemingly instant (but that depends on what happens between the message being sent on the AOL end and received on the Gmail end, and burps can occasionally occur, just like they do for non-forwarded mail) and is definitely reliable.
Only your wife can really determine how soon she'd like to terminate the original account. It's reasonably standard practice to send a message to anyone (that is, any real person) you correspond with regularly announcing that you will be dropping this e-mail address and, going forward, they should update their address lists and send messages to the new address. Some people do this but keep the original account for several months to see what comes in that they may have forgotten about (which is my practice). Others send the announcement and, after they've extracted what they want from the old account, promptly close it.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
. . . the presumption of innocence, while essential in the legal realm, does not mean the elimination of common sense outside it. The willing suspension of disbelief has its limits, or should.
~ Ruth Marcus, November 10, 2017, in Washington Post article, Bannon is right: It’s no coincidence The Post broke the Moore story