v1-3: Jeremiah's letter to those Jews who had already been taken captive into Babylon. Zedekiah sent Elasah and Gemariah to Nebuchadnezzar, and they took Jeremiah's letter along with them. Elasah’s brother Ahikam had supported Jeremiah in 26.24; and later Gemariah also supported him in 36.24-25.
v4: This was God's message to those in Babylon. He had caused them to be there. He called them to endure suffering, and to learn from it, and to turn back to Him. The content of the letter is consistent with Jeremiah’s words to the people of Jerusalem (27.12).
v5-7: Their exile was an opportunity for peace and prosperity. There is a ‘normal’ life to be enjoyed. In this respect, Jeremiah looks forward to the eternal kingdom of Heaven, when the people of God enjoy life together in the presence of God.
v8-9: The problem of false prophets; in Babylon as well as in Jerusalem. They brought words from themselves, not from God. Jeremiah provided no details of their message, but doubtless the people would recognise that Jeremiah's message differed from theirs.
It seems likely that they predicted an early return to Jerusalem; but Jeremiah's command that the people settle down contradicted that claim.
v10-14: Looking forward; their restoration to Jerusalem would be after 70 years, see 25.12; Dan 9.2. God had plans for His people in Judah, but those plans were future. He had good things for them, including a restored relationship with Himself. These things were at God's initiative, and he would accomplish what He had promised. In particular, the people would be gathered from those places He had scattered them. Even in these words, we see something of a change in their hearts, evidencing some willingness to seek God.
v15-19: Answering the prophets in Babylon, who had also prophesied concerning the people remaining in Jerusalem. Jeremiah told those in Babylon what he had prophesied concerning those in Jerusalem. He had reference to the rotten figs (24.8-10), those remaining on whom judgment would fall.
v20-23: Jeremiah boldly named two false prophets, Ahab and Zedekiah. They evidently lived ungodly lives, and spoke lies in the Name of the Lord. Their punishment was to be roasted in Nebuchadnezzar's oven (contrast Dan 3, where God delivered three faithful men from the oven).
v24-28: Jeremiah's message concerning Shemaiah followed the main letter.
Shemaiah had sent letters to Zephaniah the priest in Jerusalem. He commented that any "madman" like Jeremiah should be publicly punished. His accusation was that Jeremiah had posed as a prophet, even writing to the exiles in Babylon. (Zephaniah had succeeded Pashhur, in his role as temple guardian, see 20.1).
v29-32: The Lord's message concerning Shemaiah; he too had caused the people to trust a lie, and he too taught rebellion against the Lord. It was not just that he taught error, but he led the people to believe it.
God has the ultimate prerogative to remove those who bring error and impurity amongst His people; compare Num 16; Acts 5. The dominant attitude of rebellion seems to be the issue, rather than individual acts of wrong doing.