Did he switch jobs in the same industry? For example, did he fix cars at Joe’s Garage and now works for Goodyear. If so then he can qualify because lenders look at this as being natural. It is very common for people to get better paying jobs in the same field.
FYI: This general rule applies to graduating college students also. Yes, someone fresh out of college and on the job for a week can get a mortgage. I did this for a lawyer, who just earned his law degree, was hired by a law firm, and bought a house all in the same month.