To convert you need a forest (i.e. a set of trees where initially each node is a tree) as your temporary output structure rather than a single tree. Then on each step, rather than finding the cheapest vertex that adds a currently unconnected node to your tree, you find the cheapest edge in the graph and, if it creates a new tree (i.e. connects two previously unconnected nodes) add that tree to the forest and remove the source trees. Otherwise discard the edge.
A proper implementation of Kruskal is more memory intensive but less time intensive than a proper Prim implementation.
But the differences between the two are quite large. Probably all you can keep between are some helper functions and some data structures. Not a conversion, more a rewrite using more high level building blocks.