After I use China Construction Bank's online banking to transfer money to others, will my mobile phone receive the short message that I transfer money to others?

There is a key factor here, that is, whether you have signed a short message service agreement with China Construction Bank, that is, whether you have opened the short message notification function. If so, you can receive the change of your account in time. If not, it will not be received.

If the SMS notification function is turned on, the other party (that is, the payee) can also receive relevant news in time. For example, the other party didn't enable SMS notification, but you sent a message to it during remittance (CCB Online Banking will prompt you whether to send a message to the other party), and the other party can also receive it.