Sarah hopes to become a friend of ( ) shares her interests.

( whoever) shares her interests是宾语从句,作介词of的宾语.whoever在从句中作的是主语.
再问： 麻烦分析下整个句子的结构
再答： 整个句子是一个主从复合句。Sarah hopes to become a friend of 是主句，hopes to become是谓语动词，a friend 表语。( whoever) shares her interests是宾语从句，作介词of的宾语。