May I replace the power supply of iMac model A1225 with one from model A1419?

The bottom line? No, you cannot directly replace the power supply from an iMac A1225 (24-inch, 2007-2009) with one from an iMac A1419 (27-inch, 2012-2020). The two models have completely different power supply units (PSUs) in terms of size, voltage output, pin configuration, and overall compatibility ... so, your only available options would be to either:

• Get a replacement A1225 power supply, or
• Replace the damaged components of the existing power supply, or
• Have your friend consider replacing this obsolete Mac.

Where you should be able to find repair guides

• iFixit: Search for "iMac A1225 power supply replacement."
• YouTube: Many repair techs have teardown videos of the iMac A1225.
• Apple Forums & MacRumors: Check for threads discussing power supply repairs.

NO!!!! and this not recommended as a do it yourself as the power supply could electrocute you! PLEASE take the computer to your local Apple Authorized Service Provider to have it serviced by a qualified professional.