Extending maps from boundaries over the handlebodies - 3/4D case

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Given a map $f : \sharp^k S^1 \times S^2 \to \sharp^lS^1 \times S^2$, under what circumstances can we extend this to a map $F : \natural^k S^1 \times B^3 \to \natural^l S^1 \times B^3$?