Task Assignment between two application

If you are using UIT/DB approach you can assign the task to Group B from Group A but you need to give the permissions correctly if the user is basic user with designer access. to view the data in Application A for Group B user.

That's simple. Just assign the task to that group. There is no wall between applications, other than security settings.

I would create a group in App A and assign the task to that new group. Then make the group from App B a member of that new group. This way, you have clear a assignment approach inside App A, but can still include users or groups from the other app.

In Application A, once a user from Group A completes the task then that flow gets completed.

Tasks to Group A and Group B are not in the same flow.

For Group B there is an another process model which is in Application B.

I need to pass the task details from Application A to Application B so as to assign it to the Group B.

This is confusing ....

Did you try to just start the process in B from the process in A?

Ok, I'll try that.

you can use the start process smart service or subprocess
in the subprocess, you can call the application B Process model

You'll have to be careful here not to create a circular dependency. If Application A calls a process in Application B and then Application B calls a process in Application A you'll have problems deploying those Applications to higher environments because each will have a dependency on the other.

One way around this is to decouple the two and have them call each other via WebAPIs which are only resolved at run-time. So Application A will call a WebAPI exposed by Application B and that WebAPI can start the relevant process to create the required Task. And if you need to do the reverse then again use a WebAPI to do this.