This is resolved.
I found that in order for the Share option to be available, I must enable the Document option to "Allow Server Objects" (in addition to the already enabled option to "Allow Server Bookmarks").
Note that according to the reference manual, the option for Server Objects should goven only sheet objects (which makes sense). But in our installation, this had to be enabled else the server bookmarks could not be shared.
From the Reference Manual for "Allow Server Objects"
This check box must be enabled, if remote clients are to be allowed to create and share sheet objects with this document on the QlikView Server.