Is the teaching of Jesus before His crucifixion only for Jews?

You are absolutely correct! Adulterers, fornicators, and practicing homosexuals will not inherit the kingdom of God. If you, however, look at a woman other than your spouse with sexual desire, but change your mind soon enough you will not be counted as an adulterer.

Jesus said (before the cross) that you if you just look you are already and adulterer, but Paul (relaying Jesus' teaching after the cross) doesn't say that.

So all the apostle teaching is the same gospel Jesus tought isn't It?

When you follow through it systematically yes. As you see the older covenants fade away into the new covenant you see this seamless transition being guided by the Holy Spirit.

Paul never says anything to undermine what Jesus taught about adultery.
What Jesus said is that anyone who looks after a woman with lust in your heart you’ve committed sexual immortality. Paul never says otherwise. Finding a woman attractive is not the same as lusting after her. We naturally, and automatically, recognize beauty. We must train our eyes to not wander and we must train our mind to not fantasize about sex and we must train our “hearts” to love women as mothers and sisters and not as objects.

That is what I believe. Jesus ask the disciple preach the gospel, and we know that mean 4 gospel

Well remember, the four gospels was wrote after many of the other texts. After all Luke wrote the gospel of Luke which included the book of acts. Luke and Acts is actually one book we split apart. Acts contains way more than what Matthew, Mark and John wrote and included the acts of the apostles. We preach the good news. That’s the news preached to the lost to lead them to salvation to on. Tho use baptized into Christ goes beyond milk to solid foods. Paul was an apostle Chosen by Christ and Paul’s epistles are just as much scripture as the entire Torah and four gospels according to others.

The scholar consider 4 gospel as the document of what Jesus teach, and act is the document what the disciples did. It Seem act not only story about apostle, Stephen is not apostle but include oN the book of act.

Jesus said (before the cross) that you if you just look you are already and adulterer, but Paul (relaying Jesus' teaching after the cross) doesn't say that.

The gospels demand perfection

When Jesus told his disciples to obey the scribes and Pharisees, He had in mind only the Jews because they were still under the law of Moses.

I never hear that Jesus teaching about adultery not valid anymore

Seem to me Moses say not adultery, but Jesus say If you look woman with lust you are adultery

So what Jesus teach is not Moses law

to which man or woman healed by Christ did He say, "your perfect works & sinless righteousness have made you whole" ?

Assuredly, I say to you that tax collectors and harlots enter the kingdom of God before you

Neither have I heard that Jesus' teaching about adultery is no longer valid -- Paul confirmed them in the epistles.

Yes, you are right: Moses didn't say that husbands who look at other women are already committing adultery, but Jesus said that because he was perfecting the law of Moses.

To be saved by the Law you have to be perfect. If you look at other women with sexual desire you are not perfect and therefore cannot be saved by the Law. I could never be saved by the Law because I can't always keep from checking out girls. Yes, I do that sometimes and confess it to my wife, but thanks to the almighty God (it is not my merit) I never committed adultery.

Checking out people other than our spouses is wrong and we should avoid that because it distance us from God, but it is not so serious as adultery. Have you ever heard of a Christian who divorced their spouse because they checked out another person?

Moses say Not to adultery,

Jesus say If you look woman with lust you commit adultery

Paul say adultery not inherit the kingdom of god

So Paul law = Moses law

And you believe Jesus law only effective from the time Jesus say to the crucifixion? About 3 years and now back to Moses law?
I hear If we or our wife commit adultery, divorce is ok.

Jesus said that looking at a woman is just as serious as doing the deeds of adultery, but Paul doesn't mention "looking at a woman" -- he says that only those who commit physical adultery will not enter heaven.

If you believe that Paul's law = Moses' law, than you'll not be saved. But don't worry; Paul's teachings are actually Christ's teaching

Paul law prohibit adultery
Moses law prohibit adultery
What the different between Paul law and Moses law?

What verse that say Paul law about adultery not the same as Jesus law?

Healing depends on faith, not on having perfect works. Jesus was showing what would be necessary to be saved by the Law so that the disciples realized how impossible it was. Only after the cross Jesus would reveal the way to salvation (by grace through faith).

Jesus said that looking at a woman is just as serious as doing the deeds of adultery, but Paul doesn't mention "looking at a woman" -- he says that only those who commit physical adultery will not enter heaven.

If you believe that Paul's law = Moses' law, than you'll not be saved. But don't worry; Paul's teachings are actually Christ's teaching