This is not a good way to access one account from multiple apps, but if you insist --
-- you can long press on the account on Aqua's main screen -> options and folders -> account options -> turn off "remove deleted messages".
Since by default Aqua does not fetch complete message content when it check mail - you'll then probably want to adjust other settings to make it do that (fetch messages completely right away).
Those are:
- For message text: app settings -> network under WiFi / Mobile, "load when checking mail" and you'll want to set it to "custom size" and then 30000 (30 megabytes)
- For inline images and attachments: long press on the account -> options and folders -> preload (only for IMAP and Exchange)
But I'll say it again - this is not a good way to share an account between several mail apps. The best way is to use IMAP or Exchange and leave messages on the server (and keep "remove deleted messages" enabled).