My ball went on the wrong fairway. I intended to take a preferred lie but my playing partner said that I would be penalised a shot as I was not allowed preferred lie on the wrong fairway.
Preferred lies are a local rule, so you would need to refer to the exact wording of the rule as posted. However, if your committee is using either the R&A's or the USGA's suggested wording (e.g. from pages 128-129 of the R&A's Rules of Golf - the USGA copy is identical apart from branding), then this states:
A ball lying on a closely-mown area through the green [...] may be lifted, without penalty, and cleaned. Before lifting the ball, the player must mark its position. Having lifted the ball, he must place it on a spot within (specify area [...]) of and not nearer the hole than where it originally lay, that is not in a hazard and not on a putting green.
Note: “Closely-mown area” means any area of the course, including paths through the rough, cut to fairway height or less
and makes no mention of disallowing the use of preferred lies if you are on the wrong fairway so you would be allowed to take advantage of the rule. But again, you need to refer to the exact wording specified by your committee.
The wording of the rule specifies a mown area, as Philip mentions.
Strictly speaking, that would include any area of the course which meets those conditions which is in bounds, as a result I'd imagine that to include other fairways.
However, common sense may dictate that the mown area is designed in the rules to be indicative of an area close to the ideal target area (fairway, fringe etc) and that may rule out areas which are not close to the ideal, or intended target line.
To add further ambiguity, we have a couple of fairways which are close to fairways in the other direction, some of which give a better line to the flag which
could be specifically targeted and some which are shared, so there isn't a specific line between hole 1 and 2.
The golf rules are usually very specific to ban things which aren't allowed, so I'd probably take the approach that if it's not forbidden it's allowed! (I'd let you take a preferred lie in my group!)