To do a search for a specific tweet by user, all you have to do is go to the Twitter search bar and type in "from:@username" followed by the keywords you are looking for. This will allow you to search for tweets specifically from that user. Another option is to go to the user's profile, click on the "Tweets & replies" tab and search for keywords within their tweets. With these methods, you'll be able to easily find those important tweets by your favorite users.