It is possible to replace that connector on the motherboard, but it does require some fine skills in soldering, or microsoldering as it's being called nowadays. Generally it's done with hot air rather than a soldering iron, although once it's off you would generally clean and tin the pads with a fine tip soldering iron.
The part itself is cheap and was surprisingly easy to find; here's an example from AliExpress.
Fpc Connector Huawei Mate 10 Pro Charging
I think this is the right one, but it's hard to count the exact number of pins from your photo; you can probably do a better job with a magnifying glass. There are quite a few that come up if you search for "Huawei Mate 10 FPC connector", so pick the one with the right number of pins.
If the soldering job is out of your comfort zone (like it is mine), you can probably get a local repair shop to do the job fairly cheaply; for them, with the right tools and experience, it should be fairly simple.
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