I am an Italian with a J1 Visa. While the sponsor on my Visa is a University, my salary is paid by the non profit institute where I am conducting my research. The institute is not an accredited educational institute... still my sponsor clearly is. Does the exemption for two years apply to my situation? Moreover, I am exempted from the FICA for two years. Is this exemption valid 24 months, or only two calendar years? Thank you

This is from IRS publication 901:
A professor or teacher who is a resident of Italy immediately before the date of arrival in the United States and whose visit to the United States is expected to last no more than 2 years to teach or conduct research at a university, college, school, or other recognized educational institution, or at a medical facility primarily funded from government sources, is exempt from U.S. income tax for up to 2 years on pay from this teaching or research.
This exemption does not apply to income from research carried on mainly for the private benefit of any person rather than in the public interest.

1. You need to figure out if the research institution meets the requirement.
2. Exemption is for 24 months.

Thank you for your answer. The institute is a non profit and seems not to be an accredited educational institute . I was hoping to be able to use my J-1 sponsor (university) .