Genetic programming (GP), for the synthesis of brand new programs, continues to demonstrate increasingly capable results towards increasingly complex problems. A key challenge in GP is how to learn from the past, so that the successful synthesis of simple programs can feed in to more challenging unsolved problems. Transfer Learning in the literature has yet to demonstrate an automated mechanism to identify existing donor programs with high-utility genetic material for new problems, instead relying on human guidance. In this paper we present a transfer learning mechanism for GP which fills this gap: we use a Turing-complete language for synthesis, and demonstrate how a neural network (NN) can be used to guide automated code fragment extraction from previously solved problems for injection into future problems. Using a framework which synthesises code from just 10 input-output examples, we first study NN ability to recognise the presence of code fragments in a larger program, then present an end-to-end system which takes only input-output examples and generates code fragments as it solves easier problems, then deploys selected high-utility fragments to solve harder ones. The use of NN-guided genetic material selection shows significant performance increases, on average doubling the percentage of programs that can be successfully synthesised when tested on two separate problem corpora, in comparison with a non-transfer-learning GP baseline.