How to transfer a few text messages from one phone to another
SMS backup and restore has 


  Option to select which text conversations to backup or restore


Though it is manual and not by date . This should be fine in your case as you don't have too many



On the next screen you can select the messages manually and create a backup

Thanks to a acejavelin who pointed out that restoration can be done for a specific date range. Acejavelin further adds


  The restore process does a cleanup to remove duplicate messages