If the bow has been stored in a living space and that space is not in an arid area, the bow ought to be fine. Get a hypo kind of syringe and inject some hide glue into the delaminated spot and clamp. When the glue has cured, put a string on it and start working it. The backing will actually tighten down to the back when the bow is drawn, as long as the rest of the glue is good. That could be crumbly if it got way too dry at any time.
Don't forget the draw length is only 26". Also, 45# is pretty stiff for the average 15-year-old, especially if new to archery.
A wood bow stored inside with reasonably average humidity for 50 years will be just the same as one stored for five weeks. The moisture meter is a good idea if storage conditions for the last few months were not good or are unknown.
Jim Davis