Stratos - Good idea but don't you think he'll be getting the old birds nest after a few cast? That line will be twisted coming off one reel and onto the next. I've done this in a pinch before and it caused me more headaches than what its worth. It sucks line is so $$$$ these days and we have to do this. I wish it were more affordable.
Tight lines to all
You can actually take the spool right off the spinning reel and let the line come off as if it was a baitcaster. Birds nests on baicasters are not caused by linetwist, they are caused by over run( the spool spinning faster then your bait is traveling). Also most meduim to high end spinning reels now have an inline roller on the bail. When a reel has one you no longer should be setting a spool of line down on the ground and letting the line come off in loops as you reel it on your spinnig reel. You should do it just like you do for a baitcaster in that you stick a pencil in the spool and let the spool unwind as your reel winds it in. If done this way there should be no issues.
Edit: If you choose to just reel in the line from the spinning reel to the baitcaster the line twist you will get can be reversed , assuming you have a boat, by letting out the line behind the boat as you travel forward. the motionforward will remove all line twist. Now you simply just reel it back in.
In this situation I would personally save the braid and lose the mono and just rebuy it. WE are talking 6-7 bucks for 300 yards of berkley Trilene. that will fill that reel 2 3 times over if you use a little backing.