If you' re talking about "original" Sony PS One screen, this is "almost" unpossible lol, sorry impossible.
Because FCC cable is integrated -soldered- to screen. If you really want to lengthen it, you have to cut head -board part- of FCC cable, and you should do coercive soldering job ! But it' s very very difficult to realize.
For example; Lilliput is very flexible on this issue. Its FCC cable can be removed from both sides, very easily.
the sony or any other knock off lcd screen of that sort connects to the board using a zif connector (zero insertion force connector). If im not mistaken it is 30 pin .5 mm pitch fcc that you will need for extention. Go to lumenlab.com or diyprojectorcompany.com( i think) and they sell the extentions. Lumenlab comes with a connector to sandwhich the fcc together i don't know about the other.
How far are you trying to move the board. You may not need one if your just looking to get the board out of the way of the lcd.