Moving Large Selection of Data to Another Sheet with Formulas??

Hello! New to the forum. A coworker of mine is asking if I know how to move a chunk of selected date from one sheet to another with formulas. I know you can just copy & paste and move info into a new sheet, but he did that and then lost all of his work. Specifically, he wants to be able to sort the information and then have all that info copied into another sheet instantly. He has tried the sort and filter options, but it's taking too long and is inefficient. Is there a formula that can find/search for the cells he's looking for and then copy them into another sheet automatically? I've Googled and couldn't find anything there that was relevant.

Thanks for the help!

Dee