Future Perfect in Reported Speech

If you relate sentences in the Future Perfect,  you should first  replace "will" with "would".

a) I said: "I will have arrived..."

b) Jane said: "I will have recorded..."

REPORTED SPEECH:

a) I said I would have arrived ...

b) Jane said she would have recorded ...

Apart from that, there are some changes in time and place words.

a) She said: "I will have returned from the US by the end of this month."

b) He said: "My car will have been repaired by the next day.

REPORTED SPEECH:

a) She said she would have returned from the US by the of that month.

b) He said (that) his car would have been repaired by the following day ( or by the day after).