Did 🧙Gandalf receive a telepathic message from Manwe?

[John]

How did Gandalf the white know when he could return to the undying lands? did he get a telepathic message from Manwe? Also how did Galadriel know that she had got a pardon from the Valar before she returned to the undying lands?

 

[Erestor Arcamen]

For the first question, I think he just knew. The mission, per Appendix B:

When maybe a thousand years had passed, and the first shadow had fallen on Greenwood the Great, the Istari or Wizards appeared in Middle-earth. It was afterwards said that they came out of the Far West and were messengers sent to contest the power of Sauron, and to unite all those who had the will to resist him; but they were forbidden to match his power with power, or to seek to dominate Elves or Men by force and fear.

So Sauron was defeated and Gandalf had literally united people through the Fellowship. He also united people via most of what he did whether it was the dwarves in the Hobbit defeating Smaug or all of the people he fought alongside during the War of the Ring. Plus, unlike Saruman, he didn't sek to dominate anyone.

Not sure how she found out but from Tolkien letter 320:

Galadriel was a penitent: in her youth a leader in the rebellion against the Valar (the angelic guardians). At the end of the First Age she proudly refused forgiveness or permission to return. She was pardoned because of her resistance to the final and overwhelming temptation to take the Ring for herself.

 

[Alcuin]

In a footnote to Letter 246 concerning Frodo’s sojourn in Tol Eressëa, Tolkien describes that

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[Gandalf] was an emissary of the Valar, and virtually their plenipotentiary in accomplishing the plan against Sauron. He was also in special accord with Círdan the Ship-master, who had surrendered to him his ring and so placed himself under Gandalf's command. Since Gandalf himself went on the Ship there would be so to speak no trouble either at embarking or at the landing.​

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And in a footnote to Letter 297, he wrote,

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At the time of [Galadriel’s] lament in Lórien she believed [her exile from Aman] to be perennial, as long as Earth endured. Hence she concludes her lament with a wish or prayer that Frodo may as a special grace be granted a purgatorial (but not penal) sojourn in Eressëa, the Solitary Isle in sight of Aman, though for her the way is closed. … Her prayer was granted – but also her personal ban was lifted, in reward for her services against Sauron, and above all for her rejection of the temptation to take the Ring when offered to her. So at the end we see her taking ship.​

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Google defines plenipotentiary as

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a person … invested with the full power of independent action on behalf of their government, typically in a foreign country.​

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Moreover, Tolkien indicates (especially in Letter 156) that Gandalf died on Zirakzigil and left Eä, but was sent back into Arda by Eru. He was granted greater authority and the use of more extensive powers than he had received from the Valar. It was Gandalf who accepted Galadriel’s repentance and lifted her Exile. It was Gandalf who accepted Arwen’s suggestion that Frodo take her place in the voyage to Tol Eressëa, though it took longer for Frodo to accept the invitation, and then only after several bouts of illness.

When Sauron was defeated, Gandalf’s mission came to an end. He remained to crown Aragorn as High King of the Númenóreans, restoring the unity of the Númenórean state, and he saw the marriage of Aragorn and Arwen. These, if you will, were bonuses to his success. Thus his words to Aragorn,

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I was the Enemy of Sauron; and my work is finished.​

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