Does Fëanor really seem like the kind of person who would accept that summons? Even dead, having suddenly realised that he could not win, and his body disintegrated into ashes?
The spirits of Elves are supposed to flee from Middle Earth in terror, once Morgoth has returned there. And yet, I have difficulty imagining Fëanor fleeing anywhere, and certainly not from Morgoth.
It is hard to imagine him hearing the summons of Mandos, and obediently following it. Of all the Noldor, apart possibly from his father Finwë, Fëanor is the one who would have thought about the Halls of Mandos: about what going there meant for his own mother.
It meant losing the ability to 'do and make things and continue their experience of Arda, until released - and surely he must have known he would not be released quickly, if at all. I find it hard to accept that he'd choose that, if there was any other choice still on the table.
His sons, yes, they would go to Mandos. All of them lived long enough, and saw enough terrible things that the summons of Mandos must surely have seemed a relief. But Fëanor?
"There upon the confines of Dor Daedeloth, the land of Morgoth, Fëanor was surrounded, with few friends about him. Long he fought on, and undismayed, though he was wrapped in fire and wounded with many wounds; but at the last he was smitten to the ground by Gothmog, Lord of Balrogs...
... There he would have perished, had not his sons in that moment come up with force to his aid; and the Balrogs left him, and departed to Angband.
Then his sons raised up their father and bore him back towards Mithrim. HBut as they drew near to Eithel Sirion and were upon the upward path to the pass over the mountains, Fëanor bade them halt; for his wounds were mortal, and he knew that his hour was come.
And looking out from the slopes of Ered Wethrin with his last sight he beheld far off the peaks of Thangorodrim, mightiest of the towers of Middle-earth and knew with the foreknowledge of death that no power of the Noldor would ever overthrow them; but he cursed the name of Morgoth thrice, and laid it upon his sons to hold to their oath, and to avenge their father.
Then he died, but he had neither burial nor tomb, for so fiery was his spirit that as it sped his body fell to ash, and was borne away like smoke; and his likeness has never again appeared in Arda, neither has his spirit left the Halls of Mandos."
That last, admittedly, suggests that he is inside the Halls of Mandos. But perhaps not leaving the Halls of Mandos does not entirely imply that he ever entered them?
"Refusal had grave consequences, inevitably proceeding from the rebellion against authority" says Morgoth's Ring of the death of Elves. That could mean that he was zapped into nonexistence, I suppose, which would fit with his body falling into ash. But I don't think the Valar would have the authority to do that.
If he were unbodied, he might try to communicate with the living, but Morgoth's Ring suggests that is forbidden (forbidden when, I wonder?)
It is therefore a foolish and perilous thing, besides being a wrong deed forbidden justly by the appointed Rulers of Arda, if the Living seek to commune with the Unbodied, though the houseless may desire it, especially the most unworthy among them. For the Unbodied, wandering in the world, are those who at the least have refused the door of life and remain in regret and self-pity. Some are filled with bitterness, grievance, and envy. Some were enslaved by the Dark Lord and do his work still, though he himself is gone. They will not speak truth or wisdom. To call on them is folly. To attempt to master them and to make them servants of one own's will is wickedness. Such practices are of Morgoth; and the necromancers are of the host of Sauron his servant.
He would certainly not go to Morgoth: Fëanor hated Morgoth more than anyone else hated him. I wonder what the other possibilities are.
And I wonder who Fëanor's 'few friends' were. I think this may be the only reference to Fëanor having friends.