Hi Clarence,
The connector that broke off is part of the lightning connector assembly. The part itself isn't too expensive, but unfortunately it is a pain in the butt to replace. You'll have to remove the speaker, taptic engine, battery and logic board at a minimum in order to clear the parts that would block you from removing it.
Here's the iFixit guide you'll need to do the job
iPhone X Lightning Connector Replacement - iFixit Repair Guide
If you want to support iFixit's repair efforts you can get the part right here on this site. You can be confident of the quality of the part and they have an excellent lifetime warranty on their parts.
iPhone X Lightning Connector Assembly
On the other hand, the part can also be found elsewhere quite inexpensively on sites such as eBay, AliExpress or Amazon. Here's one example of one with a very low price.
Premium - Charging Dock Flex Cable for the iPhone X, Black - Injured Gadgets
I wrote the guide for that replacement, so if you need help along the way feel free to ask.
Need a clearer picture as in this one that part looks ok
by Nigel
@strongbow Sorry, posted extra pictures.
by Clarence Williams
I'd say ripped rather than pulverised. Remove the battery again and trace where the ribbon goes to. Replacements should be available.
by Nigel
@strongbow okay! will do, thank you for the feedback. I’ll get started on that this weekend. 😎
by Clarence Williams