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Sam thought that his wallet will have been found by one of the villagers.
Sam thought that his wallet would have been found by one of the villagers.
Sam thought that his wallet shall have been found by one of the villagers.
Sam thought that his wallet should have been found by one of the villagers.

May I ask if the version of "will/shall have been" is acceptable? (I think the version of "would/should have done" is acceptable. But I'm not sure about the other two.)

Please give me your opinion, thank you!
Comments  
Yes, possible but with a meaning different from would (which here expresses the idea that under normal circumstances, it's expected that the wallet was found, one can make that assumption):
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Will have + past participle: to express certainty or confidence about the past
Dear Sir, You will recently have received a form
Swan, Practical English Usage, will
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Viceidolif the version of "will/shall have been" is acceptable?
Not to my ear. thought that and knew that are almost never followed by can, may, will, or shall.
CJ
Try out our live chat room.
Let's start with Faulkner, shall we?Emotion: smile

Essays, Speeches & Public Letters - Page 41


by William Faulkner, James B. Meriwether - 1966

And he would rise and dress and drive in to the village; he would even drive
through the village although he knew that everything there will have long been ...

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A Place Called Mississippi: Collected Narratives - Page 123 by Marion Barnwell - History - 1997

And he would rise and dress and drive in to the village; he would even drive
through the village although he knew that everything there will have long been ...

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This first is from a document prepared seemingly for a department of the British governement:

DEVELOPMENT PUBLIC ATTITUDES TOWARDS DEVELOPMENT - July 2004

Just over one-fifth (23%) of respondents said that they thought that no progress will have been made towards this goal. ...

Zechariah

26) who have thought that hopes to this effect will have been cherished at least among some groups and that 6.9-15 refers to them; more ...

Amerasia - Page 391

For I myself have always thought that destiny will have been generous to America
if a hundred years from now historians can write of America that it was a ...

How does that compare with the corresponding frequency count for thought ... would? About the same?
CJ
No, would is much more frequent in this context than will. Thousands times moreEmotion: smile
Students: We have free audio pronunciation exercises.
Based on my analysis, the use of the shall/will have been+past participle of the verb is precisely similar to: 1) past perfect tense; e.g. She told me that she will have already got it.; 2) present perfect tense; e.g. I will have received the form lately; 3) the normal future perfect tense; e.g At that time I will have already been a lawyer.