A morph will only change the shape of an object.
It won’t change the position.
When you parent one object to another object , whaty you’re doing is connecting the positions tohether, so tht the child follows the position of the parent.
With a morph, the Positions of the “parent and child objects” don’t change, only the shape of the parent is changing
Normally, you would either create a model with Bones,. and then parent the child to a specific bone,. as Head Wax suggested.
You could also make the parent and child into one single vertex model, then delete and re-create the morph to lower the hoist and basket