The form directs you to 43. Appendix B which is the
regulation and it says :
(c) Except as provided in paragraph (d) of this appendix, for a major repair or major alteration made by a person authorized in §43.17, the person who performs the major repair or major alteration and the person authorized by §43.17 to approve that work shall execute an FAA Form 337 at least in duplicate. A completed copy of that form shall be—
(1) Given to the aircraft owner; and
(2) Forwarded to the Federal Aviation Administration, Aircraft Registration Branch, AFS-750, Post Office Box 25504, Oklahoma City, OK 73125, within 48 hours after the work is inspected.
I believe I did exactly that. plus I kept a copy for my activity sheet. as renewal is next month.