I once owned the UL6 too. Not a bad speaker but several more recent aternatives improve upon it's sound quality. Would you consider ditching the UL6 and purchasing a (working) second hand speaker? Here's one such example:
Condition is "Used". Very good condition can't see any marks on them.
www.ebay.co.uk
A very popular speaker in it's day (2010 - 2015) so plenty of them on the pre-owned market.
Reason I suggest this approach is because you could end up spending close to the original UL6 RRP (~£120 from memory?) fixing this speaker - if you send the whole speaker away for repair - whereas a better, more recent second hand speaker could cost less. If you want to keep the UL6 speakers, best bet would be to try and source a replacement tweeter and get it sent to you so you, or someone you know, could fit it. Probably involves a little soldering.
I've read that there were two versions of this tweeter, one 4 Ohms and one 8 Ohms. If that's the case, ensure you get the correct version.