I've had three cats that did that after a second house cat died. One of them, Chowder, could open cupboard doors and every night, he HAD to open every cupboard door in the house looking for the missing cat (he outlived several cats and did this at least twice that I recall). That cat is looking for it's bud and a kitten, if it fits your lifestyle, would be very good for her.
She'll fuss and stew about the kitten at first, but get along with it eventually. Chowder used to his at the new kitten and then stomp off . . . but he'd turn around to see if the kitten was watching him as he flicked his tail . . . . if the kitten wasn't, he'd go back to the kitten and bop it on the head as if it had done something wrong . . . .