Is it plausible to use other stars for the proposed FOCAL mission instead of the Sun? For some time, the far-reaching and speculative idea of using the Sun as a gravitational lens has been floating around. See this and this. This would require sending a spacecraft about ~550 AU of a distance away from Earth, so the idea is not currently realistic.

But I am wondering, is there any plausibility to using other stars (like the Alpha Centauri stars)? 

Is there there enough parallax for this to be useful? How far away must a satellite go to be able to manipulate parallax to its advantage? Are there any shortcomings to this idea that make the FOCAL proposition superior? And of course, are there any shortcomings to both propositions?

I can imagine there's not much freedom in where the so-called lens can be used, but maybe the limited field of view can still be useful if the satellite could roam the solar system?

I'm curious if anyone can give useful feedback or calculations.
Gravitational lensing works from anywhere beyond the focus, so in that sense, we could use any star as a gravitational lens. The problem is that the field of view is tiny. We only get any useful information from alpha centauri as a gravitational lens if the target object is almost exactly behind alpha centauri from our point of view. To look in a slightly different direction, we need to move a huge distance sideways. 

In fact we do use gravitational lensing from other bodies for astronomy. We use very large clusters of galaxies to amplify the images of other galaxies which lie behind them, and we watch for brief flashes as planets and stars line up for a moment as a way to detect planets (called "microlensing").