Not with POP3.
The best option is to use IMAP, this will let the app upload your sent messages to the server -- for access any time from any device, web mail, desktop mail apps, etc.
For POP3, you can use "BCC to self" (a per-account option in AquaMail, long press the account -> options and folders).
But IMAP is the way to go.
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Please also check your mail provider's web mail -- some save all sent messages independently of mail apps, on their own.