I've done this many times.
It's manual, but quick and easy, to export all linked pupil documents from SIMS.
You then need to modify each report's filename by prefixing it with the pupil's UPN. A PowerShell script and a CSV containing Admission Number and UPN can do this.
Finally, you can batch import the prepared files into Bromcom, matching on UPN in the filename (I've not tried using admission numbers because I would expect the Bromcom adnos to differ from the SIMS ones.)