Is it normal i’m still sad even though i got a new cat?

My beloved cat died a month ago.
I was not planning to get another for a while but I took a friend’s cat because her daughter is allergic.
Sweet cat, Im glad to have her but I still miss my dead kitty so much. I cry a lot and think how he used to sit on my sons lap when doing homework, guard me in the shower etc.
Should I still be sad even with a new kitty? How long is normal to grieve for a pet?