detach a process and bring into GNU screen

[Alexy Khrabrov <deliverable@xxxxxxxxx>]

I have the following funny setup on my remote server with zsh: without  
GNU screen, I can use LC_ALL=ru_RU.cp1251 and see all my Russian  
letters OK, enter them from my Mac's iTerm app fine, grep them, etc.   
However, in GNU screen, I can't enter the Cyrillics via Mac's standard  
means.

So I detach the screen to get to the bare naked zsh and do my grepping  
there.  Usually it's short.  However, occasionally I grep through my  
billion-word Russian corpus, and it takes a bit.  Sitting outside GNU  
screen means it's vulnerable to an accidental MacBook lid shut event.

Forgetting running naked grep in nohup with stdout redirected to a  
file, I wonder whether zsh can help me to put the process into  
background, detach it somehow, and reattach in a GNU screen window?   
Can I play with stderr/stdout from zsh to achieve this?

Cheers,
Alexy