It may not eat for a day or two and might lay on the ground in preparation. When ready, it will attach itself to a place where it can utilize gravity to help pull it out from the older skin. It allows gravity to do most of the work. For example the first picture shows the antennas being pulled from the original skin. The phasmid will proceed to remove its legs from the shell and then climb the skin to the top of the cage or leaf.
Phasmids have been know to consume their own skin.
The entire process can take a few hours.