Is there any link between one's ability to store information in their short term memory, with their ability to store information in their long term memory?
There is a functional dissociation between short and long-term memory.
It was observed by Milner (1966) that a patient (case H.M) can have a normally working short-term memory with an impaired long term one; and by Shallice & Warrington (1970) that a patient (K.F.) can have correct long-term memory performance while a severe impairment in short-term memory.
So there is no simple relationship between the two, if at all. Nevertheless, it could be a correlation but probably mediated by other factors such as attentional processes, explicit learning strategy etc.