In the specification, see 4.3, where it is mentioned that the Connection object can contain a unique identifier for the client and 4.3.2, which indicates ...
The purpose of a customer identifier is to associate a connection and its objects with a state maintained by the supplier on behalf of the customer. By definition, a client’s state identified by a client identifier can be “used by only one client at a time. The JMS provider must prevent clients from simultaneously using it.
Thus, it is understood here that a long-term subscription contains a unique identifier, so that when you re-subscribe an application, it can be linked to the correct state store where messages were queued in its absence. Since the preferred way to do this is to encode the identifier in the connection object for the client, the specification directs you to reconnect using the same connection, but in this case means that the object is not the same (to use WMQ terminology).
Of course, you do not need a managed object; an application can generate a connection dynamically. In this case, you will need to set the same client identifier for it for subsequent signatures.
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