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Henstock-type integrals are considered, for multifunctions taking values inthe family of weakly compact and convex subsets of a Banach lattice $X$. Themain tool to handle the multivalued case is a R{\aa}dstr\"om-type embeddingtheorem established by C. C. A. Labuschagne, A. L. Pinchuck, C. J. van Alten in2007. In this way the norm and order integrals reduce to that of asingle-valued function taking values in an $M$-space, and new proofs arededuced for some decomposition results recently stated in two recent papers byDi Piazza and Musial based on the existence of integrable selections.

Henstock multivalued integrability in Banach lattices with respect to pointwise non atomic measures