Am I religiously obligated to bear responsibility towards my colleague at work after the merchandise in his possession was stolen, and is it an injustice to make him pay for the value of the merchandise?

Your colleague is not liable for the goods entrusted to him unless he violated the terms of their safekeeping or was negligent in that regard. The basic principle is that a trustee is not liable unless there is transgression or negligence. So, if you entrusted him with your animal and asked him to keep it in a specific place (your home), but he placed it in another location (such as his car) that offers less protection than your home, then he is liable for its perishing. However, if he placed it in a similar or better protected location, he is not liable.