У вас устаревшие сведения.
В этом случае (Special Expert) от работодателя не надо ничего, кроме подписанного контракта. Последнее время, до COVID получение ВНЖ по этой схеме занимало недели, никак не месяцы. И более того - если человек подался как special expert, то он имеет право приехать сразу по туристической визе и начать работать. До получения ВНЖ.
Там есть критерии подачи на этот вид - по сути это высокая З.П. и В.О. Ну и до постоянки будет висеть ограничение по роду деятельности.
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Whether you are a specialist depends on the educational background that your work requires and the compensation paid for it.
You may be considered to be a specialist if:
Your work is demanding and requires a higher education degree.
Your salary is higher than average (at least EUR 3,000 gross pay per month).
In your application, you must prove that you meet these criteria. We use these criteria to evaluate whether you can be considered a specialist. If you do not meet these criteria for a residence permit for a specialist but still wish to apply for one, your application must clearly explain why your work is an expert task that requires expertise. For example, that the task requires expertise that you possess but that cannot be acquired by higher education and that the salary you receive corresponds with such expertise. If you show that the task is an expert task that requires expertise even though you do not fully meet the above mentioned criteria, you may be granted a residence permit for specialists as an exception.
Specialists for example include:
IT experts
experts in some field of specialisation who have a higher education degree
other persons with a higher education degree whose work requires expert knowledge
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ну и вот тут
https://migri.fi/en/specialist/en