HP Multi-Function Network Printers support is very good under Linux thanks to HP Linux Imaging and Printing (HPLIP).
But one important functionality is still missing : Scan-to-folder. You can not make your scanned documents easily available from a public network share.
This article explains how to setup a Debian server daemon to become a Scan-to-folder server for HP Multi-Function Network Printer/Scanner.
If this destination folder is shared ... you will have a direct access to your scanned documents from any PC.
This Scan-to-folder service has been tested on a Debian Squeeze server and with a HP CM1312nfi All-In-One printer/scanner.
It should be compatible with many Linux flavours and with many modern HP multi-function network printers.