Can a LocalVectorField move with its spawner?

I am emitting a particle from a ‘parent’ particle via an ‘Emitter Initial Location’ node.
The ‘parent’ particle is moving along an axis.
The issue is: the (child) particle being spawned has a local vector field within it; and although the child emits from its (moving) parent, it leaves the local vector field behind.

My question is: Is it possible to have the local vector field move along with the parent?

Anyone?..