Button that creates a group and then a component

You can create a button to do just about anything.

Be specific about the axes (not axis, singular.) Do you wish to move the component definition’s axes, or the user drawing axes when in edit mode of one of it’s instances ?

What constitutes the “lower left rear” corner ?
This description has differing results depending upon from which direction the instance is viewed.

ADD: And what is “corner” ? Is it the corner of the bounding box ? (easy)
Or is it a geometry vertex that is closest to a certain corner of the bounding box (not so easy.)
If this is a rectilinear object then things get simplier.