Background: I have an app which needs to use an intent from an other app. If this other app is not installed when its intent is needed, I would like to offer it for download and install.
Question: If the downloaded app is opened (by the user) immediately after installing it, I would need it to open the specific intent the first app needs instead of opening it as normal. See image below.
What options do I have available, is there a common pattern for this? Thanks in advance.

That is not possible, strictly speaking. There is nothing stopping the user from pressing Open, and that will behave as normal — you cannot change this.
If you are the author of the, um, “Monkey Trampoline” app, you could work out various hacks to recognize that it is being opened after an install from, um, “Animal Olympics”, so it can route its logic accordingly (use a custom sticky broadcast, have the second app use some IPC to ask the first app “yo, am I supposed to do something special?”, etc.).
It is also conceivable that
ACTION_PACKAGE_ADDEDwill be broadcast before the user clicks either Done or Open (or HOME or BACK or whatever). In that case, you could listen for that broadcast, determine that, indeed, the app just installed does involve simian somersaults, and callstartActivity(). This will be a bit jarring for the user, insofar as all of a sudden they’d be transported from the install process into this new app. And, since the precise timing ofACTION_PACKAGE_ADDEDis undocumented, your mileage may vary (e.g., the user could still get a chance to tap Open before the broadcast winds its way to your app).