If you have 13 digits for a Mexican phone number with 044 in the beginning you will have to leave out 044 which is a code used for calls to cell phones within Mexico. To the remaining 10 digits which is the actual Mexican phone number (area code + local number) you will add the following for calls from Australia: 0011 52 1. Here’s why:
-0011 is the code used to dial out of Australia (you can also use the plus sign here);
-52 is Mexico’s country code;
-1 is a digit that must be added to call Mexican mobile phones from outside Mexico.
The same rules above apply for texting to Mexico. I am not 100% sure that adding digit 1 after 52 is required for texts also (try texting without it if it doesn’t work with it).