How can I get my cat Frills, to accept & get along with our new kitten,Tabitha Two's?

Frills is the mother of our little cat Tabitha May. Tabitha May just recently Died in the gardens of the Vet Hospital. We were not going to get another cat (for a long while anyway),but when my wife went walking,she found a little kitten hearly 6 weeks old that someone had Dumped. She was all skin & bone,starving,& lying on the road near the railway tracks. My wife picked her up & brought her home,I was still in bed,& thhat's where the kitten first met me. I just howled "NO, It's too soon!",but my wife told me how she found it & put it on the bed near me. The little kitten climbed under the covers & cuddled up to my beard purring. .. She had won my heart too. I called her "Tabitha Two's",which was a nickname I called "Tabitha May" sometimes. ...... All this I have said earlier, I think. ........ What I want to know Now is... "How can I get Frills,Tabitha May's mother, to accept & get along with this little kitten?? Frills spends her nights sleeping with us(if she chooses) & the kitten gets put into a cat carry box for her safety.(& so I don't stay awake worrying about her.) In the day, the Kitten either follows us around,or curls up on me,wherever I am,even if I'm on the computer. Frills spends much of her time in the day, near her daughter's grave,or else curled up hiding somewhere. ...... Will they Ever be friends? ... We Are trying to gradually introduce them, but,, I don't know,, I just worry about them both. ....... Is there ANYTHING I can Do that we haven't tried?? .... I should add,,, My wife used to be a cat breeder & has quite a lot more knowledge than I about these things. ... But it doesn't stop me from worrying.::::::::::::::::::::: EDIT ::::::::::::::::::::: I should point out that, this new little kitten is in no way to "replace" Tabitha May or Frills! Nothing could do That! My wife & I have Told this to the cats,over & over. I even told it to Tabitha May in her grave that she is Not being replaced! ... Yes, we are both aware that this is one of the concerns of Frills; that this new kitten is to replace her daughter & her. ... NOTHING Could Ever Replace any of them! ... I just wanted to be clear on that point.