Recently in our rental house we replaced the old two conductor outlets with three conductor outlets plus a GFCI outlet at the beginning of the series. Power from the panel is connected to the 'line' side and downstream outlets are connected to the 'load' side of the outlet. Since there is no ground wire in the boxes and the boxes themselves aren't grounded we added a wire connecting the ground screw back to the neutral post. Our testers look good at each outlet and everything appears to work fine with one exception: the GFCI test button on the tester only trips the GFCI at the actual GFCI outlet. At any outlet downstream from the GFCI, the tester doesn't cause the GFCI to trip. My understanding (from this question) is that the initial GFCI outlet should also protect all the downstream outlets. This question also seems to apply but I'm not getting the same results, possibly because of the "ground to neutral" connection. Am I misunderstanding? Or have I done something wrong?
Never never NEVER connect the ground of an outlet to neutral!!! Depending on the situation, you can end up with a dangerous or even lethal voltage on the ground and therefore, on the case of something plugged in.
It is legal and advised to use a GFCI to install 3-prong outlets on an ungrounded circuit. This also applies to standard outlets downstream of a GFCI. The outlets must be labeled "GFCI protected, no ground" (labels should have been provided along with the GFCI).
You should remove all of the "bootleg" grounds.
BTW, the reason the tester didn't trip the GFCI is that it works by connecting line to ground through a resistor to simulate current leaking to ground. However, because the outlet ground is actually connected to neutral, there is no actual leakage.