From: Rabbi Moshe Sofer
To: Rabbi Yehuda
The Chasam Sofer rules that hefker (declaring an animal ownerless) can in principle exempt an animal from bechor sanctity on a Torah level, but requires actual physical abandonment rather than a mere mental declaration. He systematically rejects all proposed methods of transferring ownership to a non-Jew — including kesef, meshichah, situmta, chatzer, and gift — as insufficient to remove the kedusha of bechor, concluding that there is no valid basis to exempt these firstborn animals from their presumptive sanctity.
Source: Shu"t Chasam Sofer YD §316