Hi Florences,
Welcome to Microsoft Community. I'm sorry to hear you're having trouble with your Microsoft Surface Mouse. Regarding the authorized service centers in Malaysia, I suggest you contact Microsoft support directly and they will be able to assist you in opening a service order or provide detailed information about the authorized service centers in Malaysia. Please refer to the following steps to contact Microsoft Support: Contact Us - Microsoft Support
I hope this helps. If there is anything not clear, please do not hesitate to let me know.
Your Sincerely
Hahn. W - MSFT | Microsoft Community Support Specialist