My friend, good morning.
I'm not an expert, but from what I'm seeing the watch is apparently fake due to the placement of the engravings on the back.
The 150m/500ft engraving should be just next to the crown, with the 500ft engraving part as near it as possible, and you can see on the picture that you posted that, unfortunately, it's a bit further away than the regular ones.
You can also see that the LTD edition AT JB have the LTD edition number on the back, I did some research and could not find anyone that bought the watch from an AD or OB without a LTD edition number on the back.
You can base that assumption on this video:
Click to expand...