There are a number of ways money might have been sent abroad. But in your case it would have probably have been via a company.
Around the time that countries and empires had colonies in the Americas and Australia, companies such as Western Union started to emerge due to the increased need (or want) to send money back and forth to family members. These companies would be paid to transfer money via telegraph, this would involve having a widespread network of telegraphs working together that would "Authorize" payments rather than sending material money.
Other methods that would be less likely but still very possible in your case would be either:
- Personally, i.e someone physically took the money out to a family member.
- Through the governing body, this was very much in the interest of colonial powers as they could not only profit from transferring money but also it would mean that money was being sent out to colonies which would in turn strengthen their economies.