Did the H model have the same folding tailplane as the D. Its an obvious weak point.

A quick internet search shows an “H” with it’s fin folded. I never saw any folded during my time around the type.
Notice the photo in the OP, quite a chunk of the leading edge remains, whereas the fin folds completely flat. If it failed because of the fold feature, wouldn’t it have failed uniformly at the break?

I wasn’t aware that the folding fin was a weak point on any aircraft…several Boeing types (B-50, Stratocruiser/C-97s, KC-135s, early 707s) had folding fins, though the feature was rarely used.
Again, the severe clear air turbulence that took off that tail seemed to be a “one off” occurrence. I’ve never heard of a fleet-wide strengthening program.