Frodo has regarded Boromir as 'lost' since their encounter on Amon Hen and grieved for it. In a way it's almost a relief to hear Boromir is dead, he can do no more harm and it's a merciful release for him.
On the other hand Frodo's head must be full of appalling conjectures over just *how* Boromir came to die. A fight between the Company and its fallen member must have seemed a very likely possibility. Still Faramir's account must have been reassuring to a degree - the Orc weapons suggesting an exterior enemy.
Frodo must have been very relieved to learn the real circumstances of Boromir's death, and that he had repented and died free of the Ring's influence.
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