The letter H indicates "high breaking capacity" which I take to mean it will break above the rated value whereas the fuses rated L will likely break below that value.
So the fuse you intend to use will break around that value it's not specified. It seems than that by using the fuse you have no damage will be done BECAUSE of the rating of the fuse. The blown fuse will have blown for a reason and it will be very likely that the next fuse will also blow due to the same cause.
The specifics of your question are really a matter for the circuit designer - he will know what caused him to specify that particular fuse - the project engineer will have pressed him to have used a cheaper bog-standard 3.5A fuse - but he stuck to his professional guns. He knew what he was doing but we can only guess.
Me? I would go ahead and put in the fuse I have - it will more than likely go "pop" anyway.
Good luck...
Peccavi
March 2013