Hey
Okay - I just made a circuit with an R and a C, then linked them in parallel. Then I created a board and routed the two traces.
With both the board and schematic still open, I added my net links - these are symbols that let a net on one sheet be tied to a net on another sheet. I added two "A" links, one by the top of the R and one by the top of the C, then two "B" links at the bottoms of the R and C. Then I connected the links to the existing nets, which Eagle asked the usual "Do you want to tie this net into wire-A" etc. yes yes yes.
Then I cut the original nets between the R and C leaving each with an end tied to wire-A and the other to wire-B.
Then I closed the board.
Then on the schematic I grouped around the R and its A and B links, cut, go, then used the delete tool to delete the R and its nets and links on the schematic page.
Now I made a new sheet and pasted the R plus its nets and wire links to the new sheet.
Turning on the board, everything is intact. The resistor is still R1 as it started and it is where I left it
So, it is a lot of steps but I now have a way to move schematic sections onto new sheets. You may need a lot of "wire-n" symbols depending on what you need to move.