Weeell...that 'little piece' is the main support for the capsule, so it's kinda very important that it gets fixed....the capsule body has a fairly large weight and it can't be allowed to swing around from those wires.
Don't move it around much, only hold the capsule by the outer edge (not the centre)...and carefully place the whole shebang back in its box, being careful not to stress/stretch the wires.
If it's not a discontinued mic and parts are still available, contact the manufacturer (email these pics if necessary) and ask for a replacement support cradle/post (you should be able to fit it yourself, if you're careful).
I'm not sure how that cylindrical post attaches to the circular base plate (or if indeed the baseplate and post are one unit), but that's another 'attachment puzzle' for you to solve....and describe to those who'll supply you the part.
I suspect the screw attaching it to the capsule was over-tightened...since that's where the fracture occurred. Hence, if you get a replacement attachment post...be careful about how much tightening force you apply to any and all screws !
If the mfr doesn't reply, or the part is no longer available, you could try a 2 part epoxy glue repair at the fracture point. However, given the weight of the capsule I suspect it's going to remain a weakness, even after repair...so try for a replacement part if possible.
Whichever measure you try, in future treat the mic carefully, especially when moving and handling it...to avoid a similar fracture. I suspect the carrying box/case has received a shake or a drop at some stage, try to avoid this in future.
Best of luck..it's definitely worth attempting a repair. Don't touch either (large circular) face of the capsule with your fingers...only handle via the outer edge.
Finally...if the original mfr can't/won't supply a capsule support post or cradle, it's very likely that Matthew McGlynn at microphone-parts.com will be able to help you...here's an example of the sort of thing you'll require from his company:
https://microphone-parts.com/product...08775d82&_ss=r
The above link shows both capsule and mounting post/cradle...you only require the latter, which shouldn't cost much at all