Is good short term memory correlated with good long term memory? 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 &amp; 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.