Facebook integration has been part of XF for a long time, so from our point of view at least, it should be pretty stable.
However, we cannot guarantee the Facebook API hasn't changed significantly in that time. I seem to recall us having to make a number of changes over the years since that version was released, so alas if it doesn't work, the only solution I can recommend is to renew your license and use XF 1.5.x.
Of course, you could go with 1.3.2 and try it which might be the only way to know for sure. You could then upgrade to 1.5.x at a later date if you have issues.