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To report the gain from the sale of the partnership interest you will use Schedule D just as you would for a sale of stock or any other capital asset. As with the stock you will list the cost basis of the asset sold on the Schedule D and compute your gain from that listed cost basis.
As you know, the basis used by the taxpayer that inherited the asset is not the same as the cost basis of the decedent so this is not any problem with IRS matching.
If an estate tax return was filed for your wife the amount used for valuation in the estate tax return would be the basis for the beneficiaries as of the date of death; but there are likely adjustments that would occur between that time and the time of sale of the partnership interest.
To calculate the partner's basis use the worksheet provided in the K-1 instructions (worksheet). The "Partner's capital account analysis" section of the Schedule K-1, reports the basis to the partnership, not to the partner. The instructions for Schedule K-1 in the "Basis Rules" says:
The amount on the Schedule K-1 is the partner's capital account and may or may not be the same (or even similar in some cases) to the partner's cost basis. The responsibility for maintaining the basis of a partner's interest does belong to the partner; but you may be able to get information from the partnership or from the partnership's tax practitioner for the information needed to correctly compute the cost basis of the partnership interest. This may be complicated, or not, depending on the activity in the partnership since the date of death.
Partnership - Audit Technique Guide - Chapter 7 - Dispositions of Partnership Interest may be useful if you need details on what the IRS does look at in such cases (even though it is written primarily for audit of the partnership, and not the partner.
I hope this helps to know that there is no form other than the Schedule D to report the cost basis of the partnership interest upon disposition.