Well, if you have the code created by the other company, you might as well check how they did it. But if it's a MS Authenticator app, it's not something that can be done unattended. It essentially just means that the user who had the app set up on their phone was likely completing the challenge on their phone when needed and then the flow would continue. This is a possible solution, if the flow is not intended to run at night or weekends or other times when the user may not be available.
An API is always a better solution. Especially on web pages that have stuff in place to prevent UI automation. And MFA + reCAPTCHA are there exactly for that reason.
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