I have arduino mega and Lipo batterry such this and Lipo battery charger 5V USB Boost. I am powering arduino normally from barrel Jack with an 9 Volt adaptor. But if there is power cut occur, I dont want to stop, I want powering arduino with Lipo battery. After power come back, arduino contunie to powering from barrel jack again at the same time battery start to charge. How can I succes this. Do you have any sample circuit?
After Majenko♦ comment, I've tried circuit but there is heating problem occur. More then 70 celsius. Is that normal?