Gelfand Integral of Multifunctions

It has been proven by Cascales, Kadets and Rodriguez [J. Convex Anal. 18 (2011), 873-895] that each weak$^*$ scalarly integrable multifunction (with respect to a probability measure μ, whose values are compact convex subsets of a conjugate Banach space $X^*$ and the family of support functions determined by X is order bounded in $L_1(\mu)$, is Gelfand integrable in the family of weakly compact convex subsets of $X^*$. A question has been posed whether a similar result holds true for multifunctions with weakly compact convex values. We prove that the answer is affirmative if X does not contain any isomorphic copy of $l_1$. If moreover the multifunction is compact valued, then it is Gelfand integrable in the family of compact convex subsets of $X^*$.