Yes, Jabber Softphones do have a built in bridge. You will need to enable it. I don't know if AQM supports it as a recording endpoint or not, but from a technical perspective it shouldn't be a problem.
Ensure you have Built-In-Bridge set to "On" and not "Default", and you have the correct recording profile set on the line appearance.
Your problem is likely this, though: The recording configuration isn't configured as a global setting for the Directory Number/line, but instead is configured per-appearance. Adding it to a new device means you have to configure the recording profile on the line appearance for that device/line even after you have configured it properly for the original device.