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My wife and I have a family friend (consisting of husband, wife and two kids). My relationship with my friend's wife is very precious and I have no intention of sin. We are like sister and brother to each other. And this is known by my wife and her husband.

Is it permissible for us to hug and kiss each other on forehead? Can we ask Allah to continue this same relationship in jannah as well?

You can not touch a non-mahram.

ولا يحل له أن يمس وجهها ولا كفيها وإن كان يأمن الشهوة

It is not permitted to (even) touch the face or the hand (of a non-mahram) even when there is safety from lust

^{— الهداية في شرح بداية المبتدي [English]}

This is because Allah has forbidden even looking at them and touching is more intimate than looking.

فاسألوهن من وراء حجاب ذلكم أطهر لقلوبكم وقلوبهن

ask them from behind a partition. That is purer for your hearts and their hearts.

^{— Quran 33:53}

يا أيها النبي قل لأزواجك وبناتك ونساء المؤمنين يدنين عليهن من جلابيبهن

O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments.

^{— Quran 33:59}

قل للمؤمنين يغضوا من أبصارهم ويحفظوا فروجهم ذلك أزكى لهم إن الله خبير بما يصنعون

Tell the believing men to reduce [some] of their vision and guard their private parts. That is purer for them. Indeed, Allah is Acquainted with what they do.

^{— Quran 24:30}

And refraining from this was the way of the Prophet Muhammad (ﷺ), even though he was more pure and free of "intention of sin" and his relationship with the Muslim women was more sacred than what you describe.

ما مس رسول الله صلى الله عليه وسلم بيده امرأة قط

The Messenger of Allah (ﷺ) never touched a woman with his hand.

^{— Sahih Muslim}

The short answer is a clear and undisputed no. As already explained in the response by UmH, this is because even looking at non-mahram women is not allowed.

Beyond even the obvious evidence of the subject, I will show you a hadith narrated of the Prophet (SAW) regarding a very similar situation as yours:

Allah's Messenger (SAW) said: Beware of getting, into the houses and meeting women. A person from the Ansar said: Allah's Messenger, what about husband's brother, whereupon he (ﷺ) said: Husband's brother is like death. (Sahih Muslim)

One of the companions asks this, because he was under the impression that brother-in-laws are somehow special with their relation to women. After all, one could logically argue, they have familial pressure and are much closer to each other. The Prophet (SAW) dispels this myth and clarifies that (even) the brother-in-law is in fact a terrible source of sin.

Compare this to your situation, where you are not even a brother-in-law. If even the brother-in-law (i.e. the closest non-blood male relative to a woman) is death, what is a family friend?

no we can not not hug or kiss our non blooded sister because she is not included in our mehram the mehram which is recognized by islam is only our blooded sister ,mother,phupho,khala,grand mother and mother in law.

No it's not allowed in Islam to hug or kiss the other girl which is not your sister mother aunts grandmothers and mother in law.Only these few relations u can hug or kiss otherwise it is not allowed in Islam to touch or kiss non mahram girls.Islam says your step sister is not mahram for u and u are not mahram for your step sister. you are mahram for only your blood relations like mother, sister ,grand mother ,your mother's sisters and your mother in law. Infact u are non mahram for your cousins. So it is not allowed in Islam to touch or hug your friends wife

Not allow to touch non-mahram, even restriction for making relation with non-mahram

"O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments. That is more suitable that they will be known and not be abused. And ever is Allah Forgiving and Merciful."

"The Messenger of Allah (ﷺ) never touched a woman with his hand."

According to the definition of Islam it is not allowed to touch or even look to the non maharm this rule is for both men and women

No, it is not allow in Islam that a non mahram kiss or touch any woman. In our religion Islam, women should behave strickly with non-mahram.

Islam provides a complete code of life and insist a lot on family system, hence to create harmony in relationships it provides strict moral values. A male cannot even touch, hug or kiss a female except mehram & blood relations which are clearly defined