This lesson would (will) be much more understandable when it includes (or at least highlights) one example clearly identifying «le futur anterieur» event has occurred before some other event. There is one described in the Q and A example Cécile gives below «Nous vous téléphonerons quand nous serons arrivés = We'll call you when we get there», and some, but not all of the examples above. Many of the examples depend on an implicit, or poorly defined time sequence. With at least one well-defined example - in the lesson, not in another reference, not in the Q and A (a section which is often a mess to navigate through and too easy to miss things in - and noting that the other examples should be interpreted to include similar 'past of the future/future' pairs, this lesson would be considerably improved, in my view.
Note that in Cécile's example, and in many similar examples, English does not use the future perfect tense. This is explained in a more advanced lesson, and so probably should be avoided in this lesson.
The futur antérieur is basically the same as the future perfect in English, so I suppose it's assumed that people already know how it's used.
There doesn't have to be a second event - the tense can also be used to indicate an assumption about something that has already happened. For example: "They will have been happy together." Despite what has been said in the Q&A, this makes perfect sense to me. But I wonder if it's different in the US. I notice that Laura seems to believe that this is unique to French:
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