From the MQ documentation:
Where the MQMD includes a field that is equivalent to the JMS field, the JMS field is mapped onto the MQMD field. Additional MQMD fields are exposed as JMS properties, because a JMS application may need to get or set these fields when communicating with a non-JMS application.
The property you are looking for is probably "JMSXAppID".
If that doesn't work, check the documentation. There is a lot of weird stuff like "This section does not apply if an application uses a real-time connection to a broker." (so you don't want a "real-time connection to a broker" ... whatever that may mean).
Also "The administrator indicates that the JMS application is communicating with such an application by setting the TARGCLIENT property of the destination to MQ."
If that doesn't make sense, you must create test cases which help you figure out what MQ is doing behind the scenes. Create a JMS message, set all the properties to some weird values and send that to an inactive MQ queue where you can examine it. This way, you can figure out which field maps where.
After that works, you can try to other way around. If you JMS implementation doesn't allow you to get all properties of a message as a map or something, use the Java debugger to look at the data in memory. Field.setAccessible(true)
is your friend.