Ought I refrigerate an Inner Pot with stew inside?
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.