OK!!! To let everyone know, yes there is actually sheet music. My ex-piano teacher had one of her students play it for recital. Thats all i know about it...I need bernard or someone who has probably played or seen it to back me up!!!
Fur Elise (WoO59) was sketched in 1808, and completed either in 1809 or 1810. It was presented to “Elise” (Actually Therese Malfatti) on the 27 April 1810.
In this thread:
https://www.pianoforum.net/cgi-bin/yabb/YaBB.cgi?board=repo;action=display;num=1091424096Nana_Ama suggests that the Bagatelles WoO 60, WoO 61a and WoO 61 are “movements” of Fur Elise.
How? Why? Where do these ideas come from?

They have no relationship (musical or otherwise) whatsoever to Fur Elise. They are small piano pieces, never published in Beethoven’s lifetime. Check out the composition dates (they were composed 8 – 15 years after Fur Elise).
WoO 60 – Bagatelle in Bb – composed in 1818, its sketches are juxtaposed with the ones for the Hammerklavier, which is also in Bb.
WoO 61 – Allegretto in B minor – composed in 1821.
WoO 61a – Allegretto quasi andante in G minor was written as a souvenir for Sarah Burney Payne on 27 September 1825. It is a tiny piece just 13 bars long and like the other two has nothing whatsoever to do with Fur Elise.
Now here is my interpretation.
Whoever mentioned that Fur Elise had more “movements” was probably referring to the two “difficult” sections(bars 45 – 61 and bars 81 – 105). As you may or may not know, Richard Clayderman loves to play Fur Elise. But he only plays the first part (bars 1 – 44). So if that is what you are used to hear, when you actually hear the whole unadulterated piece, you may well be forgiven to think that it has more than one “movement”.
Either that or someone is having fun.

Best wishes,
Bernhard.