I have a sound machine that has a micro usb power adapter. The female end broke off the pcb and I want to replace the board. The picture attached shows the old board. The micro usb is just resting on the board for the picture. The power cord says 5V, .6A. I went on eBay and found something like this: https://rover.ebay.com/rover/0/0/0?mpre=https://www.ebay.com/ulk/itm/322779714089

Will this work for me?

Note: in my picture there’s also a headphone jack but I never used that so don’t need it

 

What are you existing batteries?
That board is for a LiPo cell. It may be an idea to use a 18650 LiPo cell in place of your existing battery if the circutry can stand it. And you will need to completly replace any existing charging circuitry with the new board.
Really, more info is needed.
Have you tried glueing the old socket back on and resoldering the breaks?