No, it will remain in their inbox until they delete the conversation. Instead of seeing your picture and name next to the the conversation, they’ll see a grey icon and see their name instead of your name.. like this: If they open the conversation,
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How to permanently delete Facebook from your life
Click or tap Permanently delete my account. If you'd like to delete a different account: Click or tap the username in the top-right of the Delete Your Accountpage. …
How to Delete Facebook Account Permanently Immediately
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