這里涉及到兩個問題：
第一個是單詞inform的用法.在這個句子中用的是inform sb 加that引導的賓語從句.
第二個問題就是賓語從句.賓語從句中,從句可以是陳述句,由that引導.
eg:I know that she is your sister.(that 可省略）
我知道她是你姐姐.
也可以是一般疑問句,由if或whether引導.從句要用陳述句的語序.
eg:I don't know whether she is your sister.
我不知道她是不是你姐姐.
也可以是特殊疑問句,由特殊疑問詞如what,when,how等引導,但是要注意,從句要是陳述句的語序.
eg:I am not sure when he will come.
eg:He doesn't know what her name is .
cf:He doesn't know what is her name.(這句話就是錯誤的.）
所以綜上所述,你的問題中的那句話正確的說法應該是：
Would you like to inform me whether you have received my last email?