Will the certificate be accepted for further studies by established and accredited schools

It is not accredited by the US Dept of Education. As such it is very likely no accredited school will accept credits for this school.

They are very honest and on their web page state they may not be used for licensing purpose where a degree is required to be accredited

Atlantic International University: bachelor, master, doctoral degree programs by distance learning, online, correspondence, or home study. An affordable, nontraditional, online university for adult and continuing education via distance learning allow (http://www.aiu.edu/Accreditation.html)