This touched my heart. Of course he will grieve, yes. But he still has you. You will feel very sad too, so keeping an eye on him will be a little harder at this sad time.
You have to expect him to grieve. When he does, leave him to do that for short times, then try to distract him by anything he enjoys, as have2kids said.
Don't (and I know this sounds strange)....shower him with affection whenever you see him depressed. In a dog's way of thinking, shows of affection from the 'pack leader' mean 'it's OK to feel that way/you're a good boy to feel like that'....If or when you find him like this be very normal, slightly upbeat with him, and call him to you to distract him with some walk, game, ball or frisbee...whatever. Then shower affection on him when you see his mood 'lift' a little.
I am so sorry you are facing losing your other dog like this. I know how hard it is. I have been there.
Yes, he will most likely mourn for her. Dogs can get quite depressed. He may stop eating and playing. Keep a close eye on him. Encourage him to do the things he enjoys. Also expect some regressed behavior.
It's so hard when the time comes to let them go.