Do you mean SMS texts or are you talking about notifications.
If it's SMS texts you need to be on insiders (Release preview will do) on both devices, then update Skype preview, then set the Skype preview to be your default for SMS messaging on your phone and on the PC set it to enable SMS.
Do a restart of each device and you should then see SMS messages turning up in Skype Preview on both devices, when you want to send a message if the contact is also a Skype user you can choose between SMS and Skype IM's, the conversations you have show up as different colour bars.