The general solution here is to use shell job control, and signals that replicate the key-presses. php runs in the foreground, so you launch it like so in order to run it in the background:
php -S 127.0.0.1:4444 -t /home/username/Desktop/PHP/ &
pid=$!
The assignment captures the process id of php in a variable so it can be used later.
Then you can use the remainder of your script:
sleep 20
Then if you want to terminate it you can do:
kill $pid
If you want to suspend it you can do:
kill -STOP $pid
Together this would look like this if you wanted to kill it after 20 seconds:
php -S 127.0.0.1:4444 -t /home/username/Desktop/PHP/ &
pid=$!
sleep 20
kill $pid
wait
The wait pauses the script until the kill takes effect on the php process.