Could you continue a relationship w/ someone after finding out they're having phone ?

Personally if I knew for a fact (and it sounds like you do) that this was going on and I was being lied to about it, I would give my partner the travel card. If they can't be honest enough to admit to cheating and/or having an affair with a phone operator or whatever, then how will it be if they had one with a real person. All I can say is good luck to you and I hope that you do indeed learn the truth from your partner, even if it hurts a bit at first. Then the two of you can discuss what it is that's missing in your relationship to make him spend money on pretend women.