Deleted all my POP Emails - Retrieve?

i removing pop email (with yahoo), has 5000 received , sent emails (important work) in order utilize imap instead. however, in preferences when hit '-' button, did not realize entire email storage erased (10 years of sent , receives). work purposes, catastrophe.

can emails back? can login yahoo , transfer them over? have time capsule back-up purchased , updated.

ideas? thx!!

 

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