Looking for sms forwarded notifications app

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What phone(s)? Root-ed or un-root-ed?

... Thom

Sounds like something that possibly could be done with Xposed on a rooted device. Other than that, don't think there's just an app for what you require.

Tasker ($3) can do most of what you want (paragraphs 1-3)

Tasker plus an extra 3rd party paid plugin autonotification (a few more bucks) can do all of what you want (paragraph 4).

Note when you mentioned private messaging I'm assuming it appears as a standard notification, not a popup/ float-over window. (Tasker can't see a popup window or do anything with its contents.)

1 - SMS messages – you can create a Tasker profile that fires for every incoming message and sends an SMS to any other number containing: sender, time, content. Once you have that profile set up from SMS, you can exclude SMS notifications from the remainder of your notification-handling profiles.

2 - forward notification titles only. For notifications, Tasker out of the box allows you to trigger a profile based on the “owner application” (which application sent the notification) and it gives you access to the title of the notification only (not the body text). And once the profile fires you don’t know what owner notification triggered it, other than it must be one among the set of apps identified in the profile… more later). So if you only want the title of the notification forwarded, set up one profile for notifications from all apps (excluding sms) and forward the title.

3 - Forward notification titles plus app name. Unfortunatley the above doesn’t reveal what owner application generated the notification which might be helpful contextual info for the reader of the sms. To include the owner application (along with title) in the notification you would set up a separate profile for every app that you want to intercept.

4 - Forward notification titles plus app name plus notification body text. All that work of 3 still doesn’t get you the body text of the notification (what’s below the title). There is a 3rd paid plugin for Tasker called “autonotification” (costs a few more bucks) that will give you access to the body of the notification. It will also give you access to the owner of the notification so you don’t have to set up a separate profile for each owner application as described in previous paragraph.

How much time is involved to set it up?

• If you are familiar with Tasker, then I'd say 10 minutes for #1 (I've done that one), 10 minutes for #2, a little more for #3 depending on number of applications...you can clone/modify profile for each app. Probably 30 minutes for #4 since you'd have to figure out the peculiarities of that plugin.
• If you're not familiar with Tasker, then it's tough to say how long it'll take to figure things out. I'd think about 4 hours playing around with Tasker, skimming the on-line documentation and watching tutorial videos to get basic familiarity with Tasker, then you should be able to start building the above profiles and a lot more.