After you have aquired the Ruby, go to Ruin valley. You should find a rock with a door with strange marks on it once you venture a little deeper there, use Cut to open the door, then solve the small puzzle inside the cave. Once you get on the bottom, a Rocket Scientist will take the gem and give you the second password.
My sister is still having the problem that you gave the answer to above, Smarties-kun. However, she has LF (not FR), and there is a man standing in front of the door. Would you happen to know how to get him to move? Others said she was in the wrong place, but I checked according to your description of the area. She's at the rock with the door in Ruin Valley, but the only difference from your description is the fact that a scientist is standing in the way. That's the only problem my sister is having- getting that man to move XD! Do you (or anyone else, for that matter), know how to get him to move? I apologize if I'm being a burden with these questions.