What does the 'SHARE' port on the usb expansion card do?
It is an ASUS USB3P
Looking at pictures of the card online it looks like two of the ports go to a 9-pin header and the remaining port goes to a 4-pin header.
If there is no cable on the 4-pin header then i'm pretty sure the port will do nothing. If there is a cable on the 4-pin header trace it and see where it goes.
Why it is labeled "share" I don't know for sure, maybe in the original intended configuration the port was "shared" with one of the front ports such that you could use one or the other but not both. Since I can't find any manual for this board I expect it was originally a pack-in accessory with some motherboard.
There is no 4 pin connection on the motherboard, so I assume that means it cannot be connected up?
If you had a spare USB header you could probably build an adapter cable to hook it up. You would have to figure out the pin out but that is easy enough with a multi meter.
But from some googling it looks like your motherboard doesn't have any spare USB headers so short of using a USB PCI card with an internal header or using an internal USB hub I don't see any real options for hooking it up.
Actually the 9 pin connector can handle only two USB ports so I'm thinking that the SHARE indicates an only power port, used to power old external hard disks that had two USB connectors to get enough current. You can try to charge your phone on that port, it should work.