[khr]

Translating a solution from one problem domain to another is called "transfer" in cognitive science. There's some theoretical and empirical work done on the topic of transfer (e.g. https://www.tandfonline.com/doi/full/10.1080/135467808024901...) but as far as I'm aware, there is not a mature "general theory of transfer" that can be computationally implemented. That's still in the fictional "Glass Bead Game" territory. However, you may want to take a look at that literature for broader picture theory on the issue. It's closely related to the fairly vast literature on insight problem solving, which you might be interested in.