Everyone who believes that Jesus is the Christ* has been born of God, and everyone who loves the parent loves the child.
This reminds me of the conversation Jesus had with Nicodemus, and the second half, the "everyone who loves the parent loves the child" reminds me of Jesus' words, "Jesus said to him, “Have I been with you all this time, Philip, and you still do not know me? Whoever has seen me has seen the Father. How can you say, ‘Show us the Father’? (John 14:9 )"
But as his anointing teaches you about all things, and is true and is not a lie, and just as it has taught you, abide in him.
The use of the imagery of "abiding" is similar to John's use of this term.
Yet I am writing you a new commandment that is true in him and in you, because* the darkness is passing away and the true light is already shining.
I find the poetic wording in this section similar to both the "Word of God section in John 1, and the "True vine" section in John 15.