Party B shall have the right of first refusal under equal conditions.

应该是“乙方在同等条件下享有优先购买权”吧？

youdao

Commissioning party has the right of first refusal under the same conditions.

研究开发人转让专利申请权的，委托人享有以同等条件优先受让的权利。

youdao

Second, the lessee can exercise the right of first refusal under the same conditions.

第二， 承租人可以行使优先购买权在同样的条件下。

youdao

However, if Britain wants to get rid of Gibraltar, the treaty gives Spain the right of first refusal.

ECONOMIST: Gibraltar

Like many other tech companies, Facebook holds the right of first refusal over any potential transaction on the secondary market.

WSJ: Hot Trade in Private Shares of Facebook

In return, they give Fusenet the right of first refusal to invest in any commercial venture that results from the innovation.

WSJ: The Trouble With Tinkering Time