Yes, cooked shrimp can be refrigerated. Remember, however, that it is not going to last forever in the refrigerator and you need to get it in there quick if you do not want it to spoil.
You will usually need to refrigerate cooked shrimp within about two hours after you have cooked it, but this is not set in stone. If you live in a really hot, humid climate, two hours might be too long.
On the other hand, if you live in a very cool climate, you could push this to three or even four hours.
When refrigerating your cooked shrimp, make sure you store it in an air-tight container, since this will stop bacteria from breaking down the food, or causing it to rot.
According to Still Tasty, you can also use freezer bags.
Shrimp will last up to four days in the refrigerator and up to 3 months in the freezer.
If you are planning to freeze your shrimps, then here's an answer related to best practices for defrosting shrimp: //food-drink.blurtit.com/3755161/how-to-defrost-prawns-and-shrimps