肥貓must be very happy at Rainbow Bridge now, meeting new friends and enjoying the sunshine there. He will also not be happy if he knows you are sad. Stay strong and do be happy for him, for he has gone to a better place and waiting to reunite with you.
My cat son has also gone there after a torturous battle with cancer. He has seen me through university overseas, accompanied me back to HK, getting professional qualification, meeting my husband, getting married and having my human son. When he was gone I was devastated. However, he managed to tell me through an animal communicator that he is meeting a lot of new nice friends at Rainbow Bridge, enjoying the sunshine and is no longer in any pain. I can only be happy for him. I'm sure it is the same for 肥貓 and you will want that for him too.