How to Sending SMS text messages via Skype

- Sending SMS text messages to your contact

1. Sign in to Skype.

2. Under Contacts, click the contact you want to send an SMS text message to.

3. There are two ways to send an SMS text message. You can either right-click the contact, and then select Send SMS Message…

…or, in the conversation box, click via Skype and select SMS.

4. Enter your message in the conversation box, then click the Send button.

When your SMS text message has been delivered, the “SMS: Delivered” status will appear next to your SMS text message.
If the Send SMS Message option is greyed out, this is most likely because your contact hasn’t saved a text-enabled number (usually a mobile number) in their profile. To add a mobile number to the contact, just click via SMS in the conversation window, then click Add phone 

- Sending SMS text messages to a number not saved as a contact
          You can send an SMS text message to a number not saved as a contact simply by manually entering the phone number in Skype:

1. Sign in to Skype.

2. Click the call phones icon in the Skype toolbar. The dial pad is displayed on the right side of the screen.

3. If you are texting abroad, select a country from the flag menu drop-down list, and then click in the box beside the flag.
4. Enter the phone number and click the SMS button .
5.  the conversation box at the bottom of the screen, type your message. To insert a line break, you can use the Ctrl+Enter key combination. 

       To send your SMS text message, click the Send button. Depending on your settings, pressing Enter might send your SMS text message.

When your SMS text message has been delivered, the “SMS: Delivered” status will appear next to the message. The person you sent the SMS text message to won’t be able to reply you on Skype. However, you can change your settings to receive SMS text messages on your mobile. To do so, select Tools > Options… > IM & SMS > SMS Settings and enter and verify your mobile number.

 Refer : https://support.skype.com/en/faq/FA3591/sending-sms-text-messages-windows-desktop