As Kostya pointed out, - Aquamail shows exactly the same messages as exist on the server.
So, no, there is no option to combine multiple copies of the same message.
With Gmail app, (actually, I see two possible interpretations of how things were set up there, but the effect is probably the same in both cases), - the messages, I suspect, pass through Gmail's server (cloud), where the "de-duplication" is done.
Gmail (servers) does the same if your mail client saves a "sent" message in the "Sent Mail" folder, and yet another copy arrives to your account (e.g. if you CC-ed or Bcc-ed yourself).
PS. Sorry, I didn't know what "Strato" mail meant... I had never heard that provider before.