Moving "duplicate" message to DLQ is not working when it was moved from DLQ back to original destination

Moving "duplicate" message to DLQ is not working when it was moved from DLQ back to original destination.
Use case is similar to JBPAPP-5800 but after move from DLQ to original destination I try to simulate again failing client and move message to DLQ.

Tested on EAP HQ 5.1.0 Post Relese CR2, message can't make it into DLQ.

Description:
Generate message with _HQ_DUPL_ID
Move message: original destination >>> (1) >>> DLQ >>> (2) >>> original destination >>> (3) >>> DLQ

(1) MDB with context.setRollbackOnly(); in onMessage method
(2) Move message from DLQ back to original queue, use jmx-console
(3) the same MDB like in (1) case

Move (3) fails to deliver message into DLQ, it says Duplicate message detected.

It ends with log warning [1], original destination in jmx-console shows that 1 message is in delivering state. This is again connected to JBPAPP-6080. When JBPAPP-6080 fix is present (CR3 or new nightly build) move (3) would end with exception and message would never make it into DLQ.
There would be cycle: MDB invoked severel times – try to move to the DLQ – fail, message kept in original destination – MDB invoked.

Remember there are 2 ways for (2) how to move message from DLQ (see my comment for JBPAPP-5800). Fix must work for both cases.

Possible cause:
Method moveMessage on DLQ didn't remove message's _HQ_DUPL_ID from cache of present IDs.

[1]
11:05:00,069 WARN [QueueImpl] Message has reached maximum delivery attempts, sending it to Dead Letter Address jms.queue.DLQ from jms.queue.B
11:05:00,070 WARN [PostOfficeImpl] Duplicate message detected - transaction will be rejected