Org B should have a PBS licence so will / should be listed on the register
https://www.gov.uk/government/publicati ... rs-workers
If they are not listed then the other option could be that they are part of a group on companies listed under a different name or they have only recently applied for a licence and are still awaiting the outcome.
If none of the above apply then there is a serious issue as you are in effect working illegally - in fairness it would not because of your actions but their inactive approach to obtaining a licence.
Given there were a number of ICT's transfered over (?) then you would expect the new org to be fully up to speed.