The "problems" that Matti Friedman highlights pertain to those who have followed Jewish scholarship after it reformed itself in direct opposition to Christianity around AD 100. (Generally, that would be the Protestant and Humanist societies.) Protestant translations of the Old Testament (OT) draw upon the Hebrew text preserved by the Jews that did not become Christian. The text they use is only 1000 years old; the books of the OT are at least three times that age. This text is called the Masoretic Text (MT).
The MT adopted the longer version of Jeremiah. Some minor words are different (that is, the meaning isn't changed by their variation) - that isn't a strike against them. They also added vowels (Hebrew didn't originally have vowels), which in some cases has changed the meaning of words.
How do we know the meaning of words were changed? The Greek-speaking Jews scattered around the Mediterranean at the time of Christ used a well-established Greek translation of the OT Hebrew, which is called the Septuagint (LXX). The Hebrew used in this translation is over 1000 years older than the MT, but this Hebrew text is not available anymore. Only the LXX is. The LXX not only shows what the Bible says, but it also shows how the old Hebrew text read and was understood.
The LXX had the shorter (and it seems original) text of Jerermiah. The Greek is a more specific language than Hebrew in some important cases. The LXX is what was used by the Apostles, on whom the Church is founded (Eph. 2:20), and quoted from throughout the New Testament (NT). The LXX is the basis of the Latin Vulgate used in the West by the Roman Catholics, and it remains the basis for translation of the OT in the Orthodox Church.
Thus the "missing part" from Malachi (3:5) alluded to in the article was never missing from the LXX.
Thus the differences in Jeremiah was never an issue, because the original was the one chosen for the LXX. (Scholars who favor the MT may suggest that the LXX chose a shortened, not original, text. Some have suggested that Jeremiah published two versions. It is known that some writings were published in succeeding editions by a prophet after he received new prophecies to be published. Rather than publish them separately they were put on a single scroll under the prophet's name.
The claim that a prophecy was added after the fact is ambiguously asserted. Either the author is referring to a prophecy missing from the longer version of Jeremiah in one of its manuscripts - which then is not a problem if you've only used the shorter version of Jeremiah like in the LXX - or he's claiming that it happened in a different book. In that case one would need to show an earlier manuscript without the prophecy and a later one with the prophecy; this doesn't exist.
Usually this conclusion - that something is added in after the fact - is arrived at by a "scholar" who looks at a text and decides that more than one person wrote it, even though there exists NO TEXTS that demonstrate this theory as fact. This is known as Higher Criticism, and is the generally accepted set of pre-judgments utilized in institutions of higher learning against Scripture. So when a journalist claims an unspecified prophecy in the Bible is written after the fact, it is by default an untrustworthy statement, having no textual evidence to back it up. When a "scholar" makes a claim like this, he has always been found to be assuming something he cannot prove.
Either way, the article writer is asserting that a prophecy was added after the fact, but he is not saying if that's his take or the Jews' who are presenting evidence, thus leaving the reader to assume that's just what he was told by "authorities," though that might not be the case. Which prophecy?