Hello and thanks for trusting me to help you and your pet today. I am a licensed veterinarian with over 25 years experience and would be happy work with you.
I am sorry to hear that you have lost one of your pets. It can be an adjustment for the whole household. It is totally normally for him to grieve and the length of time it will take for him to get over it is variable for every dog, but there are a few things you can do to help.
First, try to establish a new habit with him. Find something that he really enjoys be it a walk or playing with a special toy or even just grooming him if he likes that. Make it a point to engage in that behavior regularly (daily if possible) and try to make it very routine - preferably a the same time of day. This new routine will give him something to look forward to and give you and him some one on one time.
Secondly, if he is a social dog, see if you can arrange a "play date" with a friend or relative's dog. Dogs are social creatures getting him around other dogs for companionship may help him periodically, and may help you to see if he might be better off with your adding another dog to the household. Some local communities will have dog events at the park or even a doggie day care may help. He will probably do better with an adult dog friend than a puppy, but it really depends on his temperament.
There is a product called D.A.P. which is a canine pheromone. link here It creates a comforting, reassuring feeling that has a calming effect. It is a product that can be used as a room diffuser or there is even a collar available that emits the pheromone. It can be purchased through veterinarians and pet stores.
Finally, enriching his environment to help keep his body and mind stimulated may help him to start to recover. The Ohio State University Veterinary College has established a website to offer suggestions for environmental enrichment of dogs and cats. Here is a link to the website. It is filled with many great ideas. Indoor pet initiative
I hope this is helpful. Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please reply so I can clarify for you.