If it didn't work then there is something else going on.
The IRL540N and FQP13N10L are essentially the same part except:
1 -- the IRL540 is rated up to a 36 amp load and the 13N10L is rated up to a 12.8A load.
2 -- the 13N10L has about 2x 'ON' resistance of the IRL540. More resistance = more heat.

The load current won't matter. But I normally try to keep the power transistors in the same current range. It is probable that he has the circuit board traces sized for this transistor at 13 Amps (or less). If you throw in a 36 amp transistor - it is possible you can burn up a trace if you have a dead short and somebody overfused. Would rather have the transistor give up the ghost before the circuit board traces.
[Edit -- I made a misleading statement as traces are normally sized for the fuse, not the transistor. But the premise remains the same, best to have transistor burn before the trace.]

The ON resistance shouldn't matter at all unless his board uses current sensing. In that case, it would take some investigation.

Proper sub for the 13N10L is an FQP13N10L.