How can you tell her? First, you have to make a choice from three options.
A) Tell the truth.
B) Make up a story that sounds plausible, and lie your heart out.
C) Decide not to say anything to her.
Option B) always seems the most attractive. I used to take that option a lot. I was a snoop, a liar, a thief, and a cheat (with board games and card games). I can tell you, that going down road B) will never make you feel good inside about yourself. I'm secretly hoping you don't choose B).
That leaves A) and C). If you are going to tell the truth, be completely honest. There is no good reason why you went snooping, so acknowledge that fact. Own that you did something that you know was wrong. You owe your brother an apology for snooping, whether you admit it or not.
I am hoping that whether you choose option A) or C), you will see that snooping only leads to internal turmoil. Learn from this if you can. In future, whenever you get that cheeky, excited urge to snoop? Remember this. It was not worth it.
If you choose Option C), you will still know deep inside that you owe your brother an apology, and that your mother would want to know what you know. If you take this option, be very careful that your guilty feelings don't turn into resentment. Sometimes when we feel guilty inside about something, we sort of 'blame' the other people and turn the guilt into resentment... like you could resent your brother for having the beer, and your mother because you find it hard to open up to her. If you go down path C), make sure that when you find yourself overreacting and feeling overly angry at them, you acknowledge that it is actually about "the beer in the fridge".