Hi,
The German Fallschirmjäger were indeed constantly active in Italy and the Isle of Sicily from July-Aug 1943 untill May 1944 :
1.The hopeless defence of Sicily ( Jul '43 )
2.The Italian capitulation and the airdrop on the Monte Redondo ( 6 Sep '43 )
3.The rescue of Mussolini from the Gran Sasso (12 Sep'43)
4.The airdrop on the Isle of Elba ( 17 Sep '43 )
5.The battles for Monte Cassino & the defence of the Gustav Line, the battle for Anzio-Nettuno ( Jan'44 - May '44 )
If you want to know all about their airborne and ground campaigns in Italy and Sicily on first-person accounts,
buy the book : Green devils ! German Paratroops 1939-1945 by Jean-Yves Nasse,published by : Histoire & Collections Paris,
5,avenue de la République 75541 Paris, CEDEX 11- France
ISBN :2 908 182 629, Publishers number : 2 908 182
Or go to the best & most complete German Fallschirmjäger site of Greg Way :
http://www.eagle19.freeserve.co.uk/index.html
Grtz,