Thank you for your question.
What kind of partnership is this? family partnership, LLC, or simpy a proprietorship?
Tenants in common, etc?
The person who inherits the partnership interest is the one who is entilted to the adjustment to basis.
Reference this lift from regulatory guidance:
The Sec. 754 Election
Subchapter K offers a tax advantage when a successor to a decedent's partnership interest receives a basis step-up to fair market value (FMV) under Sec. 1014(a). If a Sec. 754 election is made, the successor partner can increase his share of the basis of partnership assets (i.e.,"inside" basis) by the difference between the stepped-up basis of his partnership interest (i.e.,"outside" basis) and the partnership's (lesser) basis in its individual assets. This basis increase is for the benefit of the inheriting partner only; other partners are unaffected.
However, in some situations the partnership may elect out of section K.
Please access this link and query 754 http://www.irs.gov/irb/2005-20_IRB/ar09.html