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Canonly not possible for them to trade the links of their F's with each other.

The link between the F and mage is for intensive purposes permanent. See the Find Familiar spell text. There is no text that says that the links can be swaped, exchanged like they were money or other trade goods.

Having said that. I will expand on it, by adding in some "optional" text into the phrasing equation.

There is no way to trade a familiar link with another mage; unless the mage giving up the familiar is the Optional Familiar Wrangler OCC that accompanies the optional familiar augmentation supplements in one of the Rifters.