Did the Stuka Ju-87 really have a radio altimeter? If so, when?
It looks like the actual date is 1942. The 'Nachtschlachtgruppen' aircraft were given Ju 87 D aircraft with numerous upgrades including the FuG 101 radio altimeter. 

This would make sense because to use the regular contact altimeter the pilot must have knowledge of the height of terrain above sea level and then add to that when preparing his aircraft for dive bombing. A radio altimeter should always give absolute altitude above the terrain. At night trying to estimate your height above terrain is basically impossible. It's either completely black or a sea of lights beneath you.

I found this information on page 58 of "Junkers Ju-87 Stuka", ISBN 978-83-89450-49-4. More information this book and excerpt is found here: http://mmpbooks.biz/ksiazki/46

Some brief information about the Fug 101: https://airandspace.si.edu/collection-objects/radio-altimeter-german-fug-101-1500-meter-type

https://forum.keypublishing.com/showthread.php?132745-FuG-101-Radio-Altimeter-S-101-Transmitter-Unit