My best guess is that you have a Chrysler Imperial hybrid tea rose. I suggest you look up this well known rose online to compare the foliage and bloom.  This rose also has a rich fragrance. The flowers are velvety with shapely buds and the blooms turn purplish red as they age. It is bushy and free flowering of medium height. The age of the rose is a hint to my guess of the name. In 1953, more than 65 years ago  Chrsyler Imperial was named an AARS winner and sold by many nurseries all over the US. It also comes in a climbing form. As for propagation, that would be difficult as hybrid tea roses are grafted onto a hardy root stalk so taking a cutting would not give you a hardy rose like the one you have. The good news is that this variety is still sold today.  You can order it online from www.heirloomroses.com  Gifting this same rose variety to family members is a lovely way to share a family tradition.  Keep growing, Marianne Binetti