Update: 23th October 2024

Update to Instagram v354.0 and this issue is fixed! 🥳

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Recently, Instagram launched their in-App Browser which opens all external Links directly in Instagram, which is why you may see a Screen like below:
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So basically Instagram doesn't recognize that you have WhatsApp installed, which is pitty.
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We will keep this Guide updated, once we have more info on that.

For now, we at least recommend to add a "WhatsApp Button" to your Instagram Account. Follow this Guide