If I can't finish stew in the inner pot beneath, can I place the pot (with the lid on) into the refrigerator. After 2 hours in the thermal cooker, it usually will have cooled enough. Being lazy, I'm aiming to shirk transferring the stew to a container (e.g. Glasstock). Can this refrigeration damage the pot, or spoil the stew?
No, refrigeration will not damage your inner pot. Some materials (such as ceramic) can be damaged by rapid temperature changes but the one you picture appears to be stainless steel or similar alloy and will handle temperature changes very well. Note: refrigeration is not bad for ceramic but rather going from one extreme to the other.
Please Don't leave it to sit on your counter to cool. You need to bring the temperature down for safe storage. See this answer on more about safe cooling and storage practices.
I will add a note based on the comment thread. You should not put the pot directly into the fridge immediately after removing it from the heat. This is bad for all the items in the fridge (not the pot) as pointed out by @Chris H in the comments. The solution to this is NOT to let it sit but rather to cool it off. Traditional methods are either an ice-bath or an ice wand.
You are going to need to transfer to another container to microwave so why not just do it up front. I split food up into meal sized microwavable containers. You only need to let it cool for like 10 minutes in a small container. Ideally you put it in the fridge when it gets to 140 F. The pot is easier to clean when it is warm. I don't think it is damaging to the pot. I just don't think it saves time.