As someone who used to SELL Roses for a living, I certainly would NEVER encourage propagation of Roses. ;)
But, I am retired now, so here you go! :)
Rose propagation advice from Better Homes and Gardens:
https://www.bhg.com/gardening/flowers/roses/how-to-grow-roses-from-cuttings/
Also, I’m sorry for the loss of your Mom. I’m going to be a puddle of mush when I lose mine. :(
Thank you so much for this information, Diana in Wisconsin! I’m going to follow instructions and pray I can get a rose bush out of the little cutting. Also thank you for the thoughts about the loss of my mom. It came only 8 weeks after losing my dad and was very unexpected even though she was 92. I have struggled with these losses more than I can say. Last year at this time they were both at home and doing really well. On July 3 last year, my dad fell and it was a fairly quick downhill slide. My mom fell 8 weeks after we said goodbye to my dad...a very bad fall..and was gone in 6 days. I pray your mom gives you many more years of enjoyment.