I have the next situation: A call is made to a PSTN/DID number of my phone company and that I can use with proprietary SIP cell phone app or SIP client application like Zoiper / Linphone configuring with SIP, user and password.
I cannot configure this service to forward a call to 3rd party service SIP URI. I've already asked it to my PSTN provider and they say that it is impossible.
The question is: How can I make Twilio (or maybe another service) register as SIP client with user and password (like extension/endpoint ) to receive a call from PSTN and forward it to other SIP URI or phone number?
I know that asterisk / some cloud pbx can do it like it was previously free account at pbxes.com.
Have you considered porting your number to a carrier that will allow you to forward inbound calls to a specific SIP URI you configure or register for calls to that URI, given your current carriers constraints?
For example, Twilio has some documentation here on porting a number.
I understand, based on your country, this may not be an option.
Twilio does not have a way to register as a SIP client with another provider. It does offer the ability of using a Twilio hosted number (and thus the comment on porting) to register a SIP client against or forward a PSTN call to a SIP User Agent.