Is it illegal to post his picture on the internet?

[Vivian]

These are all pictures of the criminal?

A customer is going to the authorities? This customer doesn't care about theft from your store.

Now if other people were in the background, it would be reasonable to blur their faces in the picture, though that shouldn't matter cause it would show they clearly aren't the guy, and it doesn't hurt them in any way, they don't have an expectation of privacy in the store.

You shouldn't be posting these pictures without your boss's permission though. However there is no reason to worry about privacy when these are only pictures of the robber.

The person complaining MIGHT be the robber, the police probably won't care anyways, as if somehow he gets you for violating his privacy, he would be turning himself in for armed robbery... and there is no way the DA would prosecute you.