EMB-145 Captain reported a strong fuel odor during cruise which was assigned to Maintenance upon arrival. Maintenance discovered and corrected an APU fuel leak that was misting and entering the air conditioning system.

Narrative

During climbout above 10;000 feet; the Flight Attendant called and reported a strong smell of jet fuel and that some passengers where also noticing the smell. We were avoiding a thunderstorm and a short time later I spoke to the Flight Attendant and she reported that the smell had gone away. After arriving at the gate the Flight Attendant brought it to my attention that the strong smell of jet-fuel had returned around the time of landing. At that point the smell was very evident throughout the cabin and flight deck. I wrote it up and reported it to maintenance. When maintenance came; they walked around the aircraft a few times and after the second walk around they discovered that there was fuel spraying out near the APU; at the underside of the rear fuselage. I went to have a look at the leak and there was a puddle of fuel on the ground; below the APU at this point We shut the aircraft down at that point. The next morning I noticed a strong smell of Jet fuel on my pilot shirt. Base Chief Pilot has been briefed on the event.Donning oxygen masks and returning to ZZZ would have been a consideration if the smell didn't go away; however the Flight Attendant (FA) quickly reported the smell had gone away so we continued to ZZZ1. Perhaps we should have taken the more cautious approach and don oxygen immediately. It was the trainee First Officers (FO's) second day; so that may have been a factor if the issue was present during his walk around in ZZZ. Maintenance did have issues spotting the leak however when they discovered it; as the fuel was being 'misted'. Maintenance said the fuel mist was entering the air conditioning. I spoke to maintenance later on and they changed out the fuel control unit for the APU. They said the fuel leak was close to the APU bleed valve and therefore this is how the fuel vapor entered the air conditioning system.