Hi MattRu,
Thank you for your message in this forum.
If you want to copy text box and text along with image in Word, we'd suggest you go to Home > click Select under Editing panel > click Select Objects, then you can select the image along with text box and right-click copy, then you can paste text box and text along with image elsewhere. As shown below:
At the same time, we ‘d suggest you go to Insert > Table > insert a table > then you can insert a picture and text box, as shown below:
Then you can select entire table and right-click this table > select Copy > then you can paste text box and text along with image elsewhere.
Please do let us know if that works for you, we’ll be glad to provide further help.
Best Regards,
Sukie