From Bug 580158 (where Firefox Sync was modified to work better with Private Browsing):

"Once setup, Firefox Sync will continue running even when the user is in Private Browsing mode. No data will actually be synced except data that is locally persisted in response to an explicit user request. For example, users can choose to remember passwords or store bookmarks while in Private Browsing mode. Such data will be synced. No history or tabs will be synced while the user is in Private Browsing mode."

So it appears that while in private browsing mode, if you tell Firefox to save passwords and bookmarks in Private Browsing mode, those will be synced, but history and last open tabs will not.

I also found that bug but I thought that it would be sorted out since it's from 2010. The problem is that firefox logs me out from the sync account. I have had already to re-sync this device twice. For example, I now don't even have the option "sync now" but only "setup up sync".