I don't know where the idea of a "Second Prophesy of
Mandos" comes from.
As I happen to own the 2002 book "The History of
Middle-earth Index", I can help you out.
It shows two references, HoMe volume 5 "The Lost Road", pages 324 and 333. The index of volume 5 agrees on the page numbers.
Page 324:
"The text is closely related to Q II, §§17-19, and for substantial stretches, especially towards the end, the earlier work was followed with unusual fidelity: thus for example the Second Prophecy of Mandos, with its mysterious elements, was repeated virtually without change."
This appears to be an explanatory preface to "Part Two:
Valinor and Middle-earth before
the Lord of the Rings", section VI "
Quenta Silmarillion", last sub-section "The conclusion of the Quenta Silmarillion". What then follows is the actual text.
Page 333:
"§31 Thus spake Mandos in prophecy, when the Gods sat in judgement in Valinor, and the rumour of his words was whispered among all the
Elves of the West. When the world is old and the Powers grow weary, then
Morgoth, seeing that the guard sleepeth, shall come back through the Door of Night out of the Timeless Void; and he shall destroy the sun and moon. But Eärendel shall descend upon him as a white and searing flame and drive him from the airs. Then shall the Last Battle be gathered on the
fields of Valinor. In that day
Tulkas shall strive with Morgoth, and on his right hand shall be Fionwë
{not yet Eonwë!}, and on his left
Túrin Turambar, son of
Húrin, coming from the
halls of Mandos; and the black
sword of Túrin shall deal unto Morgoth his death and final end; and so shall
the children of Húrin and all
men be avenged."