prerequisites of giving “True advice”

One of the prerequisites of giving “True advice” is that one must have no intention of trying to put the other person down.

Any good deed a person does, must be done for the sake of Allah alone.

One must speak good or remain silent. 

Giving good advice is very different from trying to put someone down. 

When someone truly cares for us, they try to advise us privately and try not to embarrass us. 

There are only certain situations in which one may advise publicly such as when it’s a very serious matter and the time to clarify the mistake is limited such as if a lot of people are present and someone said something majorly wrong and those people may leave after some time, then the correction may have to be made on the spot publicly depending on the situation. 
I don’t know fully about when exactly one can advise publicly, I need to learn more about it,
إن شاء الله 

We already know what’s right and wrong. If someone is disobeying Allah, one needs to remind them about Allah. One needs to remind them about the Power of Allah, about the Mercy of Allah, about the ni’am Allah bestowed on us, about the beautiful Names of Allah which are all beautiful, about the fact that Allah does Justice. 

A person who is righteous is not equal to a disobedient person. 

Allah doesn’t do injustice. 

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Parts of some Aayaat of the Qur’an along with Translation of the interpretation of the meaning :

.... 
قُلْ هَلْ يَسْتَوِي الْأَعْمَىٰ وَالْبَصِيرُ ۚ أَفَلَا تَتَفَكَّرُونَ
(Part of Aayah 6 : - 50) 

...Say, "Is the blind equivalent to the seeing? Then will you not give thought?"

قُلْ هَلْ يَسْتَوِي الْأَعْمَىٰ وَالْبَصِيرُ أَمْ هَلْ تَسْتَوِي…. 

….الظُّلُمَاتُ وَالنُّورُ

(Part of Aayah 13 :- 16)
....Say: "Is the blind equal to the one who sees? Or are the darknesses equivalent to the light? ....

.....قُلْ هَلْ يَسْتَوِي الَّذِينَ يَعْلَمُونَ وَالَّذِينَ لَا يَعْلَمُونَ ...
(Part of 
Aayah 39: 9)
....Say, "Are those who know equal to those who do not know?" ....