  Henstock-type integrals are considered, for multifunctions taking values in
the family of weakly compact and convex subsets of a Banach lattice $X$. The
main tool to handle the multivalued case is a R{\aa}dstr\"om-type embedding
theorem established by C. C. A. Labuschagne, A. L. Pinchuck, C. J. van Alten in
2007. In this way the norm and order integrals reduce to that of a
single-valued function taking values in an $M$-space, and new proofs are
deduced for some decomposition results recently stated in two recent papers by
Di Piazza and Musial based on the existence of integrable selections.
