As 
cracauer@ already mentioned, the key thing is to send the signal to the process group, rather than to a single process.
Just want to suggest an another way of doing this: a 
kill(1) utility can send a signal to the all processes in the group.  It is done via specifying -
PGID as pid argument, where PGID is a process group id.  You can retrieve it using 
 j option for 
ps(1): 
 ps jax will print the PGID in the 4th column.  So, bringing all that together, (let's assume your process group id is 
 4997)  
 kill -STOP -- -4997 should do the thing.  Notice this 
 -- double dash before specifying 
 -4997.  Without that, shell will treat 
 4997 as an option, whereas we, in fact, want the shell to treat the whole 
 -4997 (with leading minus) as an option.
Artem