You can receive SMS text messages in Skype if you have a Skype Number. Currently, only US Skype Numbers can receive SMS messages*. Two-way SMS text messaging is not supported in Skype on Android 4.0.4 - 5.1.
To start receiving SMS messages in Skype:
You will need a Skype Number to receive SMS messages. Learn more about how to get a Skype Number.
To stop receiving SMS messages in Skype:
SMS messages will always be enabled. To stop receiving SMS messages, you can block the specific contact or phone number.
* Note: You can receive SMS messages on your US Skype Number from US and Canadian mobile numbers. However, SMS messages sent from services such as identity verification are not supported on US Skype Numbers.