So everyone here is right, you can issue new shared no problem at all, BUT no one has mentioned tax implications.
If you gift someone shares they have to count them as income. On day 1 when you valuation is arguably $0 this is NBA. 50% of $0 = $0 but today 10% of your business at a conservative 5x multiple is closer to $200k. Might be more, might be less, but that's income and your partner needs to pay taxes on it.
This could be the worst/best gift they receive. Typically what you're describing is done with stock options. That is, granting him the right to buy shares at a future date at a fixed (low price). No matter what people tell you options != equity. You can approximate what the right number to give him are but it'll never be the same as having 50/50. If you want to give him 50% you should issues shares, but make sure you give him a big cash payout (hint: also taxed!) so he doesn't end up underwater.