Is the telephoto lens of an old camera common to the lens of a digital SLR

It depends on whether the mount of the lens and the camera are the same. If they are consistent, they can be used.

But there are some problems that can occur with older lenses when used on a digital camera, such as using a motorless lens on a Nikon D40, which has no in-body motor of its own, will have problems with not being able to autofocus, and will have to focus manually. Exactly what problems will occur will depend on your lens and body.

Of course, as a couple of people upstairs have said, as long as it's not a full-frame digital body, there's going to be a magnification conversion and the telephoto will be longer.