If I have understood it correctly, you had separate tickets and a tight "connection" ? Which in fact would not have been a connection plus normally BA won't interline bags over separate tickets, but as you have seen there are exceptions. In which case your bag may have made it to London and is now either held by BA - assuming you to be London based - or handed to Heathrow lost property, in which case there is an online item finder on Heathrow's website. If you hold a baggage tag for the missing bag identifying MUC as the end point then you would be in a slightly stronger position.

Usually BA do ask for receipts, you may find that you have some proof of purchase via your credit card online. They normally refund lost items fairly quickly, I would expect to hear from them in the next 2 or 3 weeks.