Hi gentib,
You can just drag the null-rig under the plug. I would first “zero-out” the plug and then drag the null-rig under the new parent. Animate from there.
The provided plug is along the X-axis, while the null-rig is using the Z-axis. The need to adjust this with a 90º rotation, as well as a little Z-axis adjustment. (Adjustment [move] means here, change the parent null of the null-rig). If it can be fixed directly, don’t fix it with Xpresso. Like avoiding to “fix it in post”, if it can be “done on set”.
Scene file and screen capture:
https://www.amazon.com/clouddrive/share/tiIhvNOayW8hWukXwB5DVNEch9bQNFkJOY4mlzF4zDg
You will find a file …_21.c4d as in the link. I have adjusted the axis of the plug first, so it is along the z, and with this, the Xpresso is rater simple, if Xpresso is needed. A PSR Constrain-Tag is undoubtedly a good alternative here.
However, I personally prefer the Hierarchy option from above, as it reads clearly in the Object manager, and avoids the management of Priorities.
All the best