Is there an inbuilt call recorder in an iPhone 13?

No, there is not  an inbuilt call recorder in an iPhone 13:

• Incoming and outgoing audio calls are not recorded natively on Apple's iPhones. Apple is reported to have omitted call recording owing to legal issues, despite the fact that it is not a very advanced or difficult technology to deploy.
• IntCall Call Recorder allows you to make national or international calls, record them, and save them to your phone. You'll need to use a GSM carrier and be able to accommodate both hold and conference calls. Depending on the country you're calling, IntCall may be a good option because of its pay-per-minute prices. The software works with pre-paid credit or pay-as-you-go and uses VoIP to make calls. They figure out how much each call will cost per destination and minute.

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