In fact is a discourse marker. We use in fact to add more detailed information to what has just been said: A: Did she pass her driving test? B: Yes, she did; in fact, she’s now taking an advanced driving test. In fact is commonly used in front position in a clause, although in informal situations, it may occur in end position:

The phrase "in fact" is correct and usable in written English. You can use "in fact" to introduce additional information to support a point you have previously made, or to contrast with information you have already given. For example, "I don't usually like baked goods, but in fact I really enjoy cupcakes.".