Make an object move with a dynamic parent

Select the object to be parented.
Select Edit > Group.
This parents the object to an empty group transform node.
Select Window > Outliner.
The Outliner appears.
In the Outliner, select Display > Shapes so that the Outliner displays shape nodes.
Select the shape node under the particle transform node.
Select Window > General Editors > Connection Editor.
Load the particle shape of the dynamic parent into the Connection Editor’s left side. Load the group object’s transform node into the right side.
Connect World Centroid in the left side of the Connection Editor to Translate in the right side.
This provides the dynamic parent’s World Centroid (worldCentroid) values to the Translate attributes of the group node. The World Centroid of an object is the average position of its CVs, vertices, particles, or lattice points.

In some instances, you’ll need to connect the dynamic parent’s Centroid attribute (local space) rather than its World Centroid to the group node’s Translate attribute. If in doubt, try both to see which works as desired.

Note that you can connect to any vector attributes of the group node. For instance, you can connect a World Centroid attribute to the group node’s Rotation or Scale attributes.

Note
If you do not see World Centroid or Centroid in the left column, select Left Display > Show Non-Keyable. Show Non-Keyable must be checked to view the World Centroid and Centroid attributes.
Select the child object (below the group node) and adjust its Translate X, Y, and Z attribute values as necessary to relocate it to its original position.
Play the animation.