I think you need to hold a 'family meeting' and talk about the problem. If your son admits to taking the money, tell him he first needs to tell you all WHY. Maybe in his mind, since his brother is just a little kid, he told himself he didn't 'need' the money or wouldn't miss it? (not making excuses, just saying maybe that is where his head was).
I would make him apologize to his brother and to the family. I would make him pay back the money and not allow him to buy anything for a month or two. If he does buy something, you confiscate it. If he complains about you looking in his room, explain that your family is built on trust and by stealing from his brother and lying, he has broken the family trust and lost the privilege of privacy until he can show that he is really sorry and can be trusted again.
Don't yell- make it very clear how disappointed you are and that there are real, concrete consequences to these actions BECAUSE you love him and know that this is NOT his 'best' behavior and that he can be so much better. Make it clear that there is forgiveness and a light at the end of the tunnel- but only after the apology, the consequences and the re-earning trust. Good luck.