The 77th Infantry Division was authorized two shoulder patches, for I see the classic gold Statue of Liberty on a royal blue felt background in one example, and a typical Dutch Mill in another.
The 305th Infantry Regiment had its own patch, a sort of tear shaped medallion (picture is black and white) . The 77th IDarrived Hawaii, 30 Mar 44; landed on Okinawa, 27 Apr 45; was in three campaigns,Western Pacific, Leyte and Ryukus; arrived Japan, 5 Oct 45.
The other part of the mixture would be the 98th Infantry Division, whose patch is shaped like a shield,with a red stitched border, blue felt background, and a stitched red warrier head in profile, facing to his right. There are three upright feathers, and two down in the bonnet.
The 98th ID arrived at Hawaii, 5 Apr 45; it was in no campaigns; it arrived Japan, 27 Sep 45.
If the shoulder patch I described for the 98th matches your photo, one would have to assume that somewhere along the line, your relative was involved in a change of units, which did occur at times.
It is speculation, of course, but the change of units could probably have been made stateside, and the photo would possibly depict him as a member of the 98th ID.
Please let me know if indeed we do have a match. OK ?