I was given a task to find out why a website suddenly had a drop in their organic ranking. A company specializing in SEO sent my client an email about the organic ranking drop. They had a chart showing a big drop from December 2017 to January 2018. The client has no previous records of their organic ranking or of the SEO used and updated on the website. How did this company find a chart to track my clients websites organic ranking? I am trying to use google webmaster tools and semrush to look into this since I am quite new to SEO implementation.
This very much sounds like a spam email from a person who wants to work on your client's SEO for a lot of money. I receive those continually, at times even from websites that are gone.
As for whether it did happen, if you have Google Search (you can create an account now, though, and get some info from the past) then you can see how many searches you had and see whether it indeed dramatically changed in Dec/Jan. (although I'm afraid the data doesn't go that far back anymore.)
Google Search is what shows you the organic results from Google. There is Bing Search too for Bing & Yahoo!.
A system such as Google Analytics would also show you other organic sources such as Social Media.
Now, watch out because:
(1) there are websites that are seasonal, you clients may be getting more traffic in the summer, so a slowdown around Dec/Jan would be normal
(2) there are daily/weekly/monthly patterns, I have a site that gets a lot of traffic from Monday to Friday and nearly nothing over the weekend
(3) there could have been a page that was getting a lot of traffic even though it was not producing any income for your company, just because a really influential person posted that on their social media and many users followed the link... this is most often a fad and it does not related to having good targeted traffic.
However, all of that would not allow anyone else to know about your traffic. There are only two ways for them to know: they have access to your analytics, they are part of a system such as AdSense and collect that data for themselves. Anyone else can't really know (I still don't really understand how amazon does it with their Alexa statistics, although they probably have access to some routers and gather the data from those directly...)
IMHO: If your new client's issue is Ranking and not traffic he/she is a local business.
Of course traffic does have a direct effect on Rankings.
Direct Traffic (Coming from visitors going to a website from their Bookmarks or typing in the site' URL) has become the number Ranking Factor. As well there around 100 more Ranking Factors that are considered by Google's AI Bot.
My knee-jerk reaction because you are admittedly new to SEO, you should drop the client based on no data available.
Find some low hanging fruit your degree of experience is more favorable to deal with.
Just my 2 cents worth but going for hard cases when you first start out could prove to be a very tough row to hoe at best and an exercise in futility.