Adding someone to a credit card can improve their credit score?

I was told one way to improve or build someone’s credit is to add them as a card holder on a credit card of your own. If that’s true the here’s the second question. My boyfriend wants to improve his credit and I have a few cards in my name. (I pay my bills on time and more than the minimum.) I have 2 credit cards that have a low credit limit and I have more debt on them than I have credit. I also have store charges with higher limits and not much money on them. I use them, I just don’t ever get close to maxing them out. One has a couple thousand dollar limit. My question is: What card should I add him onto? (a credit card with a low credit limit with more debt or store card with a high credit limit.) Also how do I know if this is going to show on his credit report?

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