Il aura prétendu le contraire. -- He will have been claiming the contrary.

This describes a situation where you are in the future looking back at an event, which is still in the future today but lies in the past when viewed from the future. That's exactly what the future perfect tense expresses.

It may seem to you that the English way to construct the future perfect has some elements of future tense and imperfect tense. But that is just the way it is constructed in English. It in no way implies that those two tenses can somehow substitute for the future perfect tense. Not in English and not in French either.

The examples that Nicolle gives are in the future perfect continuous (or progressive). French doesn't have any continuous tenses, so you have to use the futur antérieur for both the future perfect and the future perfect continuous.

The closest that French has to a continuous tense is the imparfait, so I can understand why you might see it as similar.

Sorry Chris I may not have explained myself very well… My issue was that in English- this tense is the future perfect progressive- and I could not see in the exercises where this particular  English tense useage was demonstrated, as falling under the  realm of futur anterior in French. So that made me question if I had missed something. It may help to have some of these English examples included in the exercises.