This should not be that complicated. But will require many code.
Thank you for your nice suggestion. I have added it to our to-do list. May be in future we will add this as core feature of this plugin.
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You can achieve this my running a cron job and query messages using FEP_Message_Query which is created more than x years ago. Then archive those messages.
You can use directly FEP_Message_Query class and pass participant_query array for both users. From the result you can determine if both have any messages between them.