Vayuu1,
I have quoted from Valmiki Ramayana [Bala Kanda, Sarga 75]. What is your source?
This is what is mentioned in verse 20 of Sarga 75- "The great Rudra handed the bow and the arrow to the Raja Rishi of Videha Devaraat." Parashurama says this line.
Then he shows the bow in his hand and says (verse 21) "This is the bow of Vishnu (capable of great conquests) and Vishnu himself handed it over to the best among Bhrigus Sage Richika, as a matter of trust."
"Then the great sage Richika handed it over to my father the great Jamadagni" (verse 22)
Then in verse 27, Parashurama asks Rama to wield the Vishnu Bow, which, he (Parashurama) repeats, has come to him through his father and grandfather.
The story that you mentioned does not feature in Valmiki Ramayanam at least.
It's in Vishnu puran as well as padam puran,even ramayana's are different with different versions,in valmiki Ramayana Sita dharti mein sama jati hai in Anand ramayan Wo Samane ke baad vapis aa jati hai.