It is possible they could find out, but it would depend on several factors. Are these schools in the same city/state/region, same tier level, etc? Does School A regularly get students from School B? If so they should be well aware what a genuine offer letter looks like and what typical financial award packages are given from School B, and may follow up with school B if something seems amiss.
Did your husband copy an actual 2018 offer letter word for word from School B and just change his name and personal information? If so, then I would say he's probably less likely to be found out, as long as he didn't put some outrageous amount. Do different award amounts correspond to specific scholarships or fellowships at School B? If so the offer letter may have different wording depending on the scholarship/fellowship awarded...Etc. There are many factors that could be considered and could impact whether he would be discovered.
I can't tell you for sure whether he will be found out or what the outcome would be. If he is found out, it is certainly possible his offer to School A will be rescinded as this could be considered a clear violation of many university's honor codes that students must adhere too. If School A found out it was forged by verifying with School B then it is also possible School B would rescind your offer. Hard determine how likely this would be without more information.