Yes, Data's information and memories were transferred, but reduced to facts and events, rather than experiences.
How do we know this?
LaForge says that Data's memories will be transferred in the jump-start procedure, but that by no means establishes that nothing else will. Since Picard accepted the procedure, one might assume it's familiar to him from "The Offspring" already - and that
procedure was described as the complete transfer of Data's brain contents over to Lal. Not just "dead" memories, but the complete contents, including experiences, personality patterns and so forth. What use Lal or B-4 would make of those is a different issue.
For all we know, Data was dumped into B-4's head in totality. How much of that overflowed and was lost, we can't tell; Data and LaForge probably wouldn't have attempted the operation unless B-4's brain had the ability to receive the essence of what was being given, though. Data clearly expects B-4 to undergo a rapid change from moron to clever android brother, and even when he's disappointed, LaForge still comforts him that this may simply take some time.