How can I recover the emails of a deleted workmail service

Unfortunately if the Amazon WorkMail Organization has been deleted, your data is not retained. See page 58 of the Amazon WorkMail Administrator Guide where it states:

If you no longer want to use Amazon WorkMail for your organization's email, you can delete your organization from Amazon WorkMail. Note This operation can't be undone. You won't be able to recover your mailbox data after an organization is deleted.

If just a single users mailbox was deleted, that could be recovered within the first 30 days before permanent deletion, unfortunately, you're pretty far outside of that window as well. This doesn't help now, but in the future, Amazon WorkMail does have the ability to export mailbox contents.