Various willows (Salix species) will produce those leaflets along the stems. Salix nigra for one; also Salix eriocephala and S. lasiolepis. And one with perhaps the most pronounced display of these leaflets is eared willow, Salix aurita, so-called because of the ear-like appearance of the leaflets. They are actually stipules and are often an identifying feature of the genus.

No pic. Try adding it in the comments. tj

I can't see the size of the vine but I imagine it could be transplanted if it's not too big. However, you don't know what the fruit quality might be like on a seedling pant and you need both male and female plants to get any fruit at all.

It's toxic to dogs. They're not likely to eat it but you never know.