Could my mother cat have the same type of cancer her daughter cat had?

I used to have two cats; a 10year old half-persian and a shorthaired 13year old who is the mother of the persian. Last November I had to put my persian to sleep because she had oral cancer and no treatment could be given due to where the cancer was when we were researching this cancer at the time we read that it could it be hereditary and that persian cats generally get these types of cancer at a early aged compared to short haired. Today I noticed my shorthaired cat was having trouble eating and was spitting bits of ham out which was what my persians symptom was when we took her to the vet where the vet said it was cancer so i am wanting to know if it is possible that my older cat has now getting it?? im going to take her to the vet asap but just want to know in the meantime. (sorry about long question)