By the time James wrote, the Jews were also dispersing as a result of persecution. I take the words he used as meant to cover all.
Surely you didn’t mean to say that Jesus was sent to save only the dispersed northern tribes and not the Jews?
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Essentially, he came to his own (Judah) and his own received him not.
They were blinded (as Paul explained in Romans)
All of the epistles were written to the people to whom Yeshua was sent.
Judah’s blindness is to expire at the beginning of their prescribed 70th week.
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Not all Jewish dispersion was the result of conquest or persecution. Plenty was nothing more than the search for opportunity elsewhere.
At the time James wrote the largest ‘Jewish’ city was probably Alexandria, Egypt. The large established Jewish colony there is why we have the Greek Septuagint.