Broken door handle
Thanks for reaching out to us! We may be able to provide you with a replacement match for the door handle you are searching for. I'll need to see a photo of the existing hardware to identify it. There are quite a few handles associated with this brand, so I wouldn't be able to narrow it down based on this information, unfortunately.
Please don't hesitate to reach out with any other questions you might have.
Thanks for the additional photos. We do not have this exact handle set but we've recommended our 82-080 Mortise Style Handle Set in the past; the keyed version of this set is the 82-081. You'll need to remove both the existing handle and its mounting plate to install the replacement.
Generally when handle sets break in this manner, it is due to excessive force being put on the handle. That said, it may be a good idea to examine the rollers and the track to see if they might need repairs as wells. At the very least, you may need to clear dirt/debris so that there is less friction.