Hi Hans,
Unfortunatly New tanks can be just as bad with a sudden algal boom as an old tank. Its not all about the nitrates. If you have just cycled and increased fish load phosphates can rise due to feeding. In fact, an algae outbreak after cycling is fairly common. Also, It could be showing only on the java moss because of the structure of the plant. With all the little fernlike bits on it, java moss catches particles and algae much easier than broad leafed plants. And yes, if you transfer water from one tank to another, the algal cells move with it!
According to George Booth:
"Thread algae
Grows in long, thin strands up to 30 cm or more. Tends toward a dull green color (hard to tell because it is so thin). Usually indicates an excess of iron (> 0.15 ppm). Easily removed with a toothbrush like hair algae."
from
http
/www.aquaticscape.com/articles/algae.htm .
Again, im not an expert, but thats not how my java moss grows, so I think it must be somthing else, and my first guess is algae.
Good Luck!
Nero