There are many variables here with regard to why your client cannot do a pushup. It is difficult for us to determine without evaluating your client. You are the best one to observe and determine the reason–then you can work on modifications.
The pushup works chest, shoulders, triceps, core, and even legs. Then, you take bodyweight into consideration, and that adds another variable. Pushup position is another factor. Here is a basic progression: Wall pushups, on knees, on toes an incline, on toes on the floor, and then on toes on a decline.
The good news is if it’s an exercise that will incorporated into a routine, then you can watch your client progress through the levels.