Dear Ms. Anderson,
Thank you for posting your request on History Hub!
We suggest that you contact the Massachusetts Archives for information surrounding the shipwreck of Anthony Thacher off the coast of Massachusetts. We also searched HathiTrust catalog and found the book Genealogy, and biographical sketches of the descendants of Thomas & Anthony Thacher from their settlement in New England June 4th, 1635 that contains a short account of the shipwreck of Anthony Thacher on page 7 and the book History of old Yarmouth. Comprising the present towns of Yarmouth and Dennis. From the settlement to the division in 1794 with the history of both towns to these times that provides an account of the immigration of Anthony Thacher on page 45.
We hope this is helpful. Best of luck with your research!