Returning to OP:
1 John 5:10-11(NASB)
The one who believes in the Son of God has the testimony in himself; the one who does not believe God has made Him a liar, because he has not believed in the testimony that God has given concerning His Son. And the testimony is this, that God has given us eternal life, and this life is in His Son.
Let us consider alternate translation choices for several of the Greek words found in this text to see if the actual message might be brought into the light of study.
1) The one who believers "in" the Son of God...
Here the preposition is "eis" meaning positionally "into" thus the phrase refers to someone who has been transferred spiritually into Christ's spiritual body. Thus a born anew and indwelt child of God.
2) has the testimony (or witness) in himself...
I believe the "testimony" refers to the gospel of our indwelt Spirit of Christ.
3) made God a liar...
Here I think the actual idea is that the one rejecting God's truth, that eternal life is in His Son, has made himself one of those who reject God's gift of eternal life.
4) has not believed into the testimony (has not been transferred into Christ's spiritual body)
Therefore when someone rejects going "all in" for Christ, they are rejecting truth and embracing falsehood.
5) God has given us eternal life
Again, the "us" refers to those God has transferred into Christ's spiritual body and indwelt, children of God.