Generating CoS under Shortage Occupation List

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A company Tier 2 A rating employer is interested in sponsoring me as Data Scientist. This job is currently under Shortage Occupations List. However in shortage Occupations List it does say
data scientist employed by a qualifying company, where the job requires a person with a minimum of five years’ relevant experience and demonstrable experience of having led a team – see notes below

In the notes it is mentioned
The sponsor must:
(a) have between 20 and 250 employees (or have fewer than 20 employees and have included the letter from UK Trade and Investment (UKTI) confirming that UKTI have been working with the company and support the application in relation to the company’s trade or investment activity); and,
(b) not be more than 25% owned by a company which has one or more other establishments in the UK, and one or more of those establishments employing more than 250 employees; and,
(c) not have been established in the UK for the purpose of supplying services exclusively to a single company or company group in the UK.
Qualifying companies can only sponsor a maximum of ten migrants at any one time in these
shortage occupation roles across all four occupations.

I have Masters in Statistics with more than 10 years experience in highly reputed companies as Data Scientist which makes me eligible for this position.

The company qualifies based on points a to c in the notes above.

Does the employer have to fill in Change of Circumstances form in order to be eligible to apply for CoS for this position.

Any other considerations for employer or employee when applying for Tier 2 visa through Shortage Occupation List.