Kokanee, you will need to stop at Evanston for inspection if it is open when you pass. If it is closed, proceed to Lucerne and launch per Utah regs. Make sure you have a Wy AIS decal if fishing Wy waters.
I have visited twice with the Green River office of WyG&F. They said that the inspection is needed upon entering Wy and before you launch in Wy. In practice, that means you must stop at all open check points you pass, and you must have a tag and certificate to launch in Wy. Keep the tag and certificate with you on the boat in case you are checked on the water or at take out.
If you are staying in Wy for a bit after an inspection entering the state, keep the certificate and seal with you until you leave and that will allow you to launch multiple times while in Wyoming. In case of checks at the launch or takeout, I think that I will also make sure to keep a receipts (e.g., camping receipt for Buckboard) to confirm that I have not left the state since the inspection. Still, even if staying in Wy and having the tag and certificate from your original entry, you must stop at any check point you encounter while traveling or at the launch. Inspectors might then choose to reissue a tag and certificate.
That is my understanding, but do your own checking.
