If you have sent SMS message from Skype, but your contact didn't receive it and you were charged then it's important that you report this to customer service for investigation as follows:
1) Open your SMS history: https://secure.skype.com/account/call-history
2) Write down the number/date/time of the failed SMS message
3) Check with your contact who is their mobile service provider
4) Ask your contact if they were roaming(abroad)
5) Did your contact by any chance recently ported their number to new provider?
5) If possible try to send SMS from a mobile to check if number is able to receive SMS message in order to rule out any possible temporary mobile service provider issue
Once you have all this information please forward it to customer service either via email or chat support as guided here: https://support.skype.com/faq/FA1170
It's important that you include all the requested information, otherwise customer service can't investigate it with carriers.
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