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I am sorry to hear about this situation. The "old" management company may be afraid of what they see as your "personal information" being released to the new management company. This may be unfounded, but it is the most likely cause.
SECOND, understand that the old management company does not have to provide any signature or information unless they want to. No law states that the old landlord/their management company has to confirm your good payment record.
The best way here would be to kill two birds with one stone by writing a certified letter to the old management company (CC landlord themselves if possible), that explains both (1) you do not mind the information being released and (2) nicely ask that it is.
This does two things - it (1) allays the fears that you would be upset at any records being released and (2) it asks nicely, and being nice in such situation is crucial because they do not have to do this, so you are asking them for extra work.
Let me know if you need a sample letter!
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