And we know that the Son of God has come and has given us understanding, so that we may know him who is true; and we are in him who is true, in his Son Jesus Christ. He is the true God and eternal life. -- 1 John 5:20 (ESV)

Here John is writing about both the Father and the Son simultaneously in one verse. He attempts to explain how we should relate to both, but unfortunately out of context the "him", "who" and "he" words made it unclear whom is whom and this is where the confusion comes in. Unlike the modern English bibles, the original Greek manuscripts were all written in capital letters. The choice of capitalized and lowercase words in the bible depends on the translators' understanding.

The previous verses are:

We know that everyone who has been born of God does not keep on sinning, but he who was born of God protects him, and the evil one does not touch him. We know that we are from God, and the whole world lies in the power of the evil one.

It is clear the focus is on "God". The "Son of God" is not yet mentioned because John's focus is on why we need "God".

And we know that the Son of God has come and has given us understanding...

Meaning John is about to reveal a revelation from the Son of God not about the Son of God. Let's see what they understood:

... so that we may know Him Who is true;

It is more likely that this Him is referring to the God of the previous verses, i.e. he is saying "The Son" gives us understanding of "The Father" which is inline with Matthew 11:25-27.

... and we are in Him Who is true ...

It is more likely that the second Him is still referring to the previous Him otherwise John would have indicated that he is changing the subject.

The word "in" in the Greek translation according to Strong's Concordance means:

Original Word:     ἐν
Part of Speech:    Preposition
Transliteration:   en
Phonetic Spelling: (en)
Definition:        in, on, at, by, with

In other words it seems like John is trying to say "we have 'access' to God" (being "at" or "by" God), but how?

... "in" his Son Jesus Christ.

This is also inline with Galatians 3:26, Galatians 3:28, John 15:1-9 and Romans 8:1

To put it together in my own words:

"We know that the Son of God has come and has given us understanding that we may know the Father Who is true; and we are 'with' the Father (Who is true) 'through' His Son Jesus Christ".

He is the true God and eternal life.

John already said twice that "God is true", why would he suddenly change the subject in this verse? It is more likely that he is making the point that "because we have 'access' to the true God, we will also have access to the eternal life". This links to the theme of the previous verses of 1 John 5:11-19.