Quote from the app's FAQ-page:
https://www.aqua-mail.com/search/?q=ArchivArchiving messagesSupported for IMAP / EWS accounts, not POP3
1. Choose or create your archive folder:
2. Long press on the account -> options and folders -> folders
• For Gmail: use Gmail -> All Mail
• For Fastmail, iCloud, maybe others: use pre-created Archive
• For the rest: if there is no archive type folder, tap the “+” icon to create one
1. Tap the chosen folder, choose “Sync as Archive” or “Archive, don’t sync”
2. Assign a swipe gesture for message lists, if wanted: app settings -> swiping -> scroll down to “message list”
3. Assign notification icon, if wanted: app settings -> message notifications -> action icons. I recommend “Delete or archive, depending on the account” if some of your accounts will have “archive” and some won’t.