There are various ways by which a person can start his business in India. A firm, which you are referring to is a Limited partnership firm or a LLP , which is of one of such forms. A Privated limited Co. is another such form. So basically, you need to apply for conversion of the present partnership to Pvt. Ltd. Co. You can take help of a Company Secretary to do the same. For this, it is required to have atleast two directors and a minimum paid-up capital of Rs. 1 Lakh.
As far as, benefits available to employyes are concerned, they are in accordance to various applicable Labour and Industrial laws in this regard and also as per the Business Entity's its own policy. As long as its under private ownership, nothing wou;d be affected by such a conversion.
I hope I'm clear and solved your querry.