Question: Is it gramatically correct to say THEY SHALL; if so in which context? 

Answer: Very people carefully observe the complicated distinctions between "shall" and "will" -- which are made much MORE complicated by the fact that in traditional use, the senses of each word used with the first person are "flipped" when used for the second and third persons.\n\nIn general, you probably do not need to worry about using it.  But in case you run across someone saying or writing "they shall" here's what to do with it (assuming they are using it correctly and not just acting snooty!) \n\n"you/they will" is a simple future tense (statement of fact)\n"you/they shall"  implies something more, usually a guarantee (certainty) or obligation.\n\nIf you are familiar with the King James Version (or something like it) of the Ten Commandments and the Sermon on the Mount, you have plenty of good examples.\n\nThink, for instance, of command forms like "Thou shalt not" (modern "You shall not" or "Do not").  These express an obligation or demand.  Or consider the ending of each of the Beatitudes.  Each implies a promise/certainty ("they shall inherit the earth", etc. ) with the implication that the SPEAKER is certain or will make certain that it happens.    So, as an assurance, you might say (fomally) "They [you]  shall have what they [you] seek."  (Compare the biblical "Ask and you shall receive...")\n\n(Conversely with the first person.  Traditional "I shall" was the simple future, and "I will" was a strong statement of purpose/certainty, sometimes of WILL-fulness!  Think of someone  insisting, "I don't care what anyone says. I WILL find a way to do it.")
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