What that means is you have effectively demonstrated the Truth through apologetics.
That all sounds good, but how responsible might I be if that person begins to doubt their faith, but stays with it anyway, in spite of it being proven false. If he is unwilling to look for the truth, and to challenge his previous faith, his soul, as I believe it, would be in jeapardy.
You cant expect someone to convert overnight…so when you say “but stays with it anyway” that doesnt mean they are not thinking about what you said, rather it can often mean you started them thinking and as they continue to look into the various issues and comparing both sides (even without telling you) they could be on the road to coming home (even if they dont know it until the last minute!).
There is NOTHING worse than finding out you are in serious error, especially in regards to your theology…to some its just too shocking to change.
Further it is very dangerous to change religions overnight, St Paul warns about those who are unstable/weak in their faith and are “blown around by every new wind of doctrine” that comes around. It is better for people to convert for the right reasons, that way when they become Catholic they wont have the tendency to abandon ship the second a problem comes around. There have been converts on these forums who were not quite prepared and as a result were shifting in and out of serious doubt about their faith, it is a sad sight :(.
Somehow, would I be partially responsible for him?
As long as you are properly represented the Catholic Church you are doing your duty. If he never converts its not your problem.