Tip #1: I suggest to open the Replicator page in your Notes and manually activate/replicate the line “Sending outgoing mail” (or named similarly, I do not see it actually)
Tip #2: In your Notes client, open your current “Location” and check the “Mail” tab, if the “Mail file location” is “Local” then change it to “On Server” for the sake of test. Also check the “Send outgoing mail” field, and if it is “directly to Internet” than change it to “Through Domino server”. I suppose you CAN access your Domino server with your Notes client.
Please inform me about the experience. HTH