When transferring money to someone else on a mobile phone, can China Construction Bank send messages on the mobile phone?

Yes, just leave a note for the transfer, but the other party must enable the SMS notification function.

The postscript for transfer and remittance is used to explain the purpose of the transfer. The word limit is as follows: the professional version can enter 25 Chinese characters (i.e. 50 letters or numbers); the public version/mobile banking can enter up to 20 Chinese characters, letters or numbers; 16 Chinese characters can be filled in at the counter; 30 Chinese characters can be filled in at the visual counter. Warm reminder: There cannot be special characters in the remarks.