It depends on the base.
I just found this out the other day (credit goes to locdawg) - a standard house light bulb has whats called a medium base. All standard light sockets in your house are going to be medium base.
So, does your 125w fixture hold a standard incandescent light bulb? If you can screw a regular old light bulb into the 125w fixture your friend gave you - then you got a medium base socket in the fixture.
Okay, let's assume it's a standard medium base.
What kind of base is on the 300w bulb you're wanting to use? Look it up. If it's a mogul base or some other weird E26 base - then the answer to your question is - NO - it won't work in that socket that your friend gave to you.
The other concern is the reflector on the socket. Even if the 300w CFL is a medium base, it still has the big plastic chunk near the end. Thats the ballast. Some people have reported problems using really large CFL's in reflectors because the plastic housing that surrounds the ballast is so large that you can't get it down into the fixture deep enough to even screw it in.
If you can take the reflector off, then it might work. A lot of the clamp-on reflectors will unscrew.
First, I'd figure out what kind of base is in the reflector you've got and then figure out what kind of base the 300w bulb has. If they don't match up then there's no point in bothering.