Yahoo has been gaining search share, thanks to a partnership it forged with Mozilla near the end of last year. Google has taken note and is now lobbying for Firefox users to switch their Yahoo's Bing powered searches out for its own search.

Google doesn't appear to be making appeals to all Firefox users. But for those who search out Google's engine, the company is offering them instructions on how to dump Yahoo.

"Switch your default search engine to Google," states the alert launched at Firefox users who turn to Google for search result.

The message is followed by a "Learn how" button which walks users through the process of lifting up Firefox' hood, unplugging Yahoo search and attaching the cables to Google.

Back in November of 2014, Yahoo and Mozilla revealed their partnership and stated that Yahoo's Bing-infused search would become native to Firefox.

"This partnership helps to expand our reach in search and gives us an opportunity to work even more closely with Mozilla to find ways to innovate in search, communications, and digital content," said Yahoo CEO Marissa Mayer back in November.

While users can switch out Yahoo for Google search at anytime, Yahoo has already been benefiting from those who can't be bothered to do so. Firefox' Yahoo integration began in December, with delivery to the U.S., and then rolled out worldwide this year.

Since partnering with Mozilla, Yahoo's share of the search market has risen for a bit. However, Yahoo's rise hasn't been more than a full percentage point and its approximately 6.5 percent slice of the global market is still dwarfed by Google's roughly 58 percent stake, according to NetMarketShare.

Stateside, the Yahoo and Mozilla's partnership had a slightly more pronounced effect on Google's share of the market. The roughly 77 percent share of the market in Google held in November fell by about two points and has stabilized for the last few months, while Yahoo saw a bump of approximately two points, according to Statcounter.

While Yahoo nibbles out Google's slice, it may not seem like a big deal. Mozilla's partnership with Marissa Mayer's company sends a threat on another front. Mozilla has severed its dependence on Google for search services and it may be seeking to retake some of the market share it lost to Chrome.

Chrome has twice the market share of Firefox and is second only to Microsoft's Internet Explorer, which comes pre-installed on every piece of Windows hardware.