I know iOS is very strict about accessing sms and user data. But I wish to implement simple feature, something like log.
In my app user sends sms to another number (robot). And gets it’s state back in sms. I know I can’t access them in any way. But maybe I can set up a button which would simply show sms from certain number if there are any. Just to open Messages for a certain number that’s all.
Is that possible, and can be accepted by Apple?

You can only send an sms. You cant view any messages. Check the apple documentation here.
Apart from usage of
MFMessageComposeViewController, only option you have is to open the message app as,Or just to pop up the sms app with number as,
Here is a similar question.
Update:
If you want to do this inside your app, you can use
MFMessageComposeViewController. Check this apple documentation for more details on this.