I'm going by the released memo postet in this thread in full length and the NY Times article that is roughly characterising the so called 'Demo memo'. My take is that this is all the information that is out there and I'm basing my statement on them. From what I gather the dem memo is disputing the amount of information the FBI provided (it says that is was more than the Nunes memo claimed) but it does not say that the FBI provided all the info.
That is ofc assuming the FBI knew about the financing, even if it happens to have started with Republican money.
Who I think signed it off is not important. Both the memo (first page, at the end of the 3rd paragraph) and the NY Times article state the FISA extension was at least once signed by Rosenstein:
Edit: The link to the NY Times article:
https://www.nytimes.com/2018/02/02/us/politics/trump-fbi-memo.html?smid=tw-nytpolitics&smtyp=cur