On Roblox's site it says: "After a purchase is made, it’s your responsibility to handle and record the transaction" Is it mandatory to save the transaction? If I don't what will happen?
You do not need to save developer product transactions. However, I strongly recommend that you do it. Roblox does not keep a track of purchases made with developer products, so this is the developer's task.
Just make sure you're Granting the purchase so that you receive what the player has spent and that the player does not get a refund and an item / other things in the game.
I recommend that you save the purchases made in case you want to verify that a player actually has bought something. (You never know when you need it, unless you already do ;-;)