Push notifications

i am running OpenWRT with a 4G usb stick. I can send/receive sms messages by making use of the sms-tool app. I would like to get these messages pushed via email, telegram or whatever service to my mobile. Is there any way to do that?

Do you have an internet connection? If yes you can use one of these smtp clients

Yes, the machine has Internet access (4G) and i am already using the ssmtp with a gmail account. i am able to send emails from CLI. So the question is, how do i forward the received SMS to my email?

create a script that will poll the SMSes and resend them as emails, telegrams, or whatever ?

that i s what i am looking for

and that you will have to create, AFAIK there's no such package.
shouldn't be rocket science though ...

start by looking into the smstools3 package.

What protocol does you modem support? AT-ccomands, QMI or MBIM?

Not sure about the commands, i got to check. It is a Huawei 3372s

It uses AT commands

I have a similar script, but you need to verify two AT-commands.
Can you paste the response from:

AT+CMGR=<one of the the idexes above>

(Yes, CMGD is delete message, but with =? it will list all messages)

Use picocom to access your modem.