Hello BluChange,
Let's use the steps below to double check your settings for text message forwarding:
1. On your iPhone, iPad, or iPod touch, go to Settings > Messages > Send & Receive. On your Mac, open Messages, choose Messages > Preferences, then click iMessage. Make sure that you're signed in to iMessage with the same Apple ID on all your devices.
2. On your iPhone, go to Settings > Messages > Text Message Forwarding.*
3. Choose which devices can send and receive text messages from your iPhone. If you're not using two-factor authentication for your Apple ID, a verification code appears on each of your other devices: enter that code on your iPhone.
As long as your iPhone is turned on and connected to Wi-Fi or a cellular network, new SMS/MMS texts can be sent and received on the devices that you added.
You can also find those steps in this resource: How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support
Should that still persist, do you forward your messages to any other devices? If so, are they exhibiting the same behavior?
Also, does restarting both your iPhone and Mac have any impact on this behavior, even if only temporarily?
Restart your iPhone - Apple Support
Shut down or restart your Mac - Apple Support
Let us know, and we'll keep moving forward from there.
