Be aware most carriers can allow this to work but usually don't by default.
The carrier rejects the call because they see the CLID of the original call as not being a valid billing number on the PRI, therefore invalid and the call is rejected. They can usually set the PRI to allow these calls, and if the CLID is invalid, they substitute the main telephone number for billing purposes thus allowing the call and the appropriate CLID to be displayed. Run into this all the time with Mobile Extension sending out the original caller's CLID information on a PRI.
BTW, what's a 5530 set???
(Just kidding, I am sure its a typo)