Well before being a few months? Nintendo purchased Retro mid-2002. The same year Metroid Prime came out. The switch from third to first person happened long before that.

Nintendo purchased the rest of Spangenberg's shares in mid-2002 however an article from IGN suggests that Nintendo had ownership since 2001 ... 

What's more is that the cited source on the wiki page for Retro Studios says it was a subsidary for Nintendo since 2000 but since the source has likely been updated it looks like I'll never know ... 

Besides most of the development for Metroid Prime occured within a year just before it's release date when the employees were pushing 80-100 hours for each week to get the game done ...

To start with, that article is a retrospective. The 2001 could have been a mistype. Considering that an article reporting the news from gamespot was published May 2nd 2002. I highly doubt they were a year late on this news. 

Another IGN article retrospective also suggests that they were bought in 2002, saying "Earlier in the year[2002], president Spangenberg sold his shares of Retro to Nintendo, which effectively became the majority stockholder." 

As for what you said about them purchasing the shares, you do know how shares work don't you? Or are you suggesting Nintendo already owned some stock in the company? But that wouldn't matter because that wouldn't put them as the owners. Plus, a former retro studios dev also made it clear that the $1 Million was all nintendo had to spend on the company.

The sited source on the wiki says nothing about the date like you said. The wikipedia page could be talking about the year Retro first partnered with Nintendo. 

But, that's irrelevant, because it was switched to a first person perspective in 2001. There's some footage from Spaceworld 2000 that shows the perspective, but I can't find a direct link to that, so this will suffice.

It has to be:
From Sofware + Retro Studios
or
From Software + Kojima Productions