Is a cash inheritance included in MAGI for calculating Medicare Part B payments?. Will increased payments go back down in future years?

A cash inheritance that is not in a tax deferred account of some type is not taxable and not entered on your tax return. It is therefore not included in the MAGI for calculating Medicare Part B payments. 

If the inheritance was in a tax deferred account and you take a distribution, the amount of the distribution that is taxable would be entered on your tax return and included in the MAGI.

Your income for purposes of increased Medicare premiums is recalculated each year. For example: 2017 premiums are based upon 2015 income; 2018 premiums are based upon 2016 income.
<a rel="nofollow" target="_blank" href="https://www.ssa.gov/pubs/EN-05-10536.pdf">https://www.ssa.gov/pubs/EN-05-10536.pdf</a>