not that i am the brightest tool in this box, having admitted my ignorance on the issue already.
however, the way i understand this, "porque" in this particular case is a noun: "reason". hence "el porque" = "the reason". "the reason he gave it away". i guess that in english you could also say "the reason for him to give it away" (which is what you are aiming at here) but that would not roll off my tongue easily.
personally i would go with "la razón" because the first rule i learnt at school is to go with the structures and expressions you know and understand even if they are simple. it's better to use simple language and be understood than aim too high and mess up