Thanks Mike,
Back in 2017 Kostya posted this
"Re: push
For push mail, for "Internet Mail" (IMAP) accounts, Aqua Mail uses the industry standard, well documented, widely supported "IDLE" extension.
It is supported/used by: Gmail, AOL, Hotmail, Yandex, GMX, Fastmail, Web.de services and others, and also servers like Dovecot, Courier, Cyrus and others."
That was in this thread
https://www.aqua-mail.com/forum/index.php?topic=5673.msg34487#msg34487However I take your point that techies can get transitions wrong and this seems to be what has happened here. I got an email back from AOL overnight and their main rebuff is to beware of third party email applications. With that in mind I re-activated my K9 that I had used before I heard about Aquamail and it cannot get my wife's account to recognise the IDLE.
I think I will have to accept that it may not be corrected by AOL.
Whilst digging for the solution I read several times on this forum about how much more battery power is used by IDLE compared with doing a frequent sync. With that in mind I have moved from IDLE to a five minute sync. I can live with that delay. Would you agree that my battery will be benefitting.
The other extremis solution is to move the whole email address which is my wife's name @compuserve.com to my own UK based server that I trust. Is it possible to migrate/move a full email address with the @ to a server that is nothing to do with the words after the @. Google is far from clear. What is your view?
Thanks for your interest and help so far. Aquamail is brilliant. I wish I had come across it earlier and not wasted so much time with other software.