Recent experiments demonstrate transfer of lipid molecules between a charged, supported lipid membrane (SLB) and vesicles of opposite charge when the latter adsorb on the SLB. A simple phenomenological bead model has been developed to simulate this process. Beads were defined to be of three types, 'n', 'p', and '0', representing POPS (negatively charged), POEPC (positively charged), and POPC (neutral but zwitterionic) lipids, respectively. Phenomenological bead-bead interaction potentials and lipid transfer rate constants were used to account for the overall interaction and transfer kinetics. Using different bead mixtures in both the adsorbing vesicle and in the SLB (representing differently composed/charged vesicles and SLBs as in the reported experiments), we clarify under which circumstances a vesicle adsorbs to the SLB, and whether it, after lipid transfer and changed composition of the SLB and vesicle, desorbs back to the bulk again or not. With this model we can reproduce and provide a conceptual picture for the experimental findings.