The migrating carbon originally bonded through its positive lobe but for the reaction to occur it must go through the negative lobe and form a sigma bond. It is clear from the transition state diagram that inversion occurs.

So in thermal suprafacial [1,3]-migration Configuration of the migrating group will undergo inversion.

The migrating carbon originally bonded through its positive lobe, in the tranistion state and the product this is retained. It is clear from the transition state diagram that retention occurs.