Boromir's body was never recovered, at least not by Faramir.
The Two Towers, Book IV, Ch. 5 The Window on the West:
[Faramir, speaking to Frodo (and Sam)] ‘I sat at night by the waters of Anduin, in the grey dark under the
young pale moon, watching the ever-moving stream; and the sad reeds
were rustling. So do we ever watch the shores nigh Osgiliath, which
our enemies now partly hold, and issue from it to harry our lands. But
that night all the world slept at the midnight hour. Then I saw, or it
seemed that I saw, a boat floating on the water, glimmering grey, a
small boat of a strange fashion with a high prow, and there was none
to row or steer it.
‘An awe fell on me, for a pale light was round
it. But I rose and went to the bank, and began to walk out into the
stream, for I was drawn towards it. Then the boat turned towards me,
and stayed its pace, and floated slowly by within my hand’s reach, yet
I durst not handle it. It waded deep, as if it were heavily burdened,
and it seemed to me as it passed under my gaze that it was almost
filled with clear water, from which came the light; and lapped in the
water a warrior lay asleep.
‘A broken sword was on his knee. I saw
many wounds on him. It was Boromir, my brother, dead. I knew his gear,
his sword, his beloved face. One thing only I missed: his horn. One
thing only I knew not: a fair belt, as it were of linked golden
leaves, about his waist. Boromir! I cried. Where is thy horn? Whither
goest thou? O Boromir! But he was gone. The boat turned into the
stream and passed glimmering on into the night. Dreamlike it was, and
yet no dream, for there was no waking. And I do not doubt that he is
dead and has passed down the River to the Sea.’
Then turning again to Frodo, he
spoke in a quiet voice once more. ‘To those questions I guess that you
could make some answer, Frodo son of Drogo. But not here or now,
maybe. But lest you still should think my tale a vision, I will tell
you this. The horn of Boromir at least returned in truth, and not in
seeming. The horn came, but it was cloven in two, as it were by axe or
sword. The shards came severally to shore: one was found among the
reeds where watchers of Gondor lay, northwards below the infalls of
the Entwash; the other was found spinning on the flood by one who had
an errand on the water. Strange chances, but murder will out, ’tis
The shards of Boromir's horn were returned to their father, Denethor. There's no mention of who, specifically, retrieved the shards from the river and brought them to Denethor.
The Return of the King, Book V, Ch. 1 Minas Tirith:
‘He would have gone,’ said Gandalf. ‘Be not unjust in your grief!
Boromir claimed the errand and would not suffer any other to have it.
He was a masterful man, and one to take what he desired. I journeyed
far with him and learned much of his mood. But you speak of his death.
You have had news of that ere we came?’
‘I have received this,’ said
Denethor, and laying down his rod he lifted from his lap the thing
that he had been gazing at. In each hand he held up one half of a
great horn cloven through the middle: a wild-ox horn bound with
‘That is the horn that Boromir always wore!’ cried Pippin.
‘Verily,’ said Denethor. ‘And in my turn I bore it, and so did each
eldest son of our house, far back into the vanished years before the
failing of the kings, since Vorondil father of Mardil hunted the wild
kine of Araw in the far fields of Rhûn. I heard it blowing dim upon
the northern marches thirteen days ago, and the River brought it to
me, broken: it will wind no more.’ He paused and there was a heavy
silence. Suddenly he turned his black glance upon Pippin. ‘What say
you to that, Halfling?’
There's no record that Boromir's body was ever recovered by anyone. The Elvish "magic" of the boats from Lorien may have allowed the boat to pass unseen and unmolested down the river and out to sea.
The Fellowship of the Ring, Book II, Ch. 8 Farewell to Lorien:
‘Heed the words!’ said the other Elves. ‘These boats are light-built,
and they are crafty and unlike the boats of other folk. They will not
sink, lade them as you will; but they are wayward if mishandled. It
would be wise if you accustomed yourselves to stepping in and out,
here where there is a landing-place, before you set off downstream.’