It can be helpful to try to imagine what the person who died would tell you if you could talk to them. Or just contemplate your own death and how you would want people to react to it.
I will NOT want people, no matter how close they are to me, to get drawn into despair. Think about me fondly if they wish, get together and swap stories and memories, contrast the world with me and the world without me, sure.
But I don't want anyone to withdraw from their own life and become less than a whole person. That would not honor my memory, that would make me responsible for a terrible tragedy that I was by definition unable to do anything about.
I have lost my share of close ones, and when it happens I always talk about it with my first dog, who died many years ago. You can have a conversation with a dog that you might not be willing to have with another person because dogs never judge you.
When your dog dies (and this is a serious dog person speaking here so pay attention) you feel bad and you miss him. But "dog" is not just an identity, it's a job. When any job becomes vacant, it must be filled. You still need someone to keep the sofa in shape when you're too busy to do it, to tell you how silly you are, to remind you of life's priorities. So you get a new dog and he makes you happy without lessening your love for the old dog.
People aren't so different. They each perform a service in your life and if one of them leaves to take a job in Estonia or simply dies, you still require that service.
No dog does the job quite the way the previous dog did, but you get adjusted to each other. No one can relate to you the way a spouse or parent or child or sibling did, but you need to fill that gap in your life with SOMETHING. This is one situation in which it's okay to fill a round hole with a square peg. Eventually you won't be so conscious of the shape of the hole because you'll appreciate the qualities of the peg.
I know that all of my dear departed dogs would be glad to see that I'm not still consumed with grief, because all they ever wanted for me was to be HAPPY. And they would feel downright HONORED to find that I found what they added to my life to be so utterly essential that I still need someone to keep doing it.
That's the way I feel about my friends and loved ones. I want them to be happy now, and when I'm gone I still want them to be happy. And if they find someone new to provide what I provided, it must mean that what I provided for them turned out to be really important and that makes me feel good too.
Celebrate your loved one. Respect their wishes by continuing to live the life they wanted you to have. And honor them by allowing yourself to admit that the spot they filled in your life was so important to your happiness that you can't leave it empty.