I'm sorry to hear that your kitty has tapeworms.

I adopted Sky from the Humane Society and he had been a stray and had fleas which they treated with advantage. Unfortunately they never dewormed him which they should always do for a stray. About 3 months later I found a little wiggly worm where Sky had been sitting and even saw one wiggling out of his bottom. I was terrified and hoped that none of my other cats would get infected.
The vet gave me 4 drontal pills. He was given 2 at the vets and then I had to give him 2 more about 3 weeks later. He's been fine ever since and none of my other cats have tapeworms. Before all of this happened he had also had his stool tested for worms and it was negative. Now if I ever adopt a stray or a cat that hasn't already been dewormed, I'm going to make sure that my vet gives them some pills to take care of all types of worms.

Goodluck. I'm sure everything will work out fine. My vet thinks that Sky must have swallowed a flea when he used to have fleas and that's how he got the tapeworm.