The question, as clarified in a comment, is I just want to make sure that if it is weird to put "responsible for" in the sentence like first and second in question.
I will interpret the question to be: given this sentence
Mr Robert is responsible for X task.
where X is some task or job duty, for example proofreading all outgoing quotes, can the sentence be rewritten in the form
There is X task which Mr Robert is responsible for.
The answer is that yes, in principle you can do this, but "There is" is awkward. Here are two example sentence to give you a feel for the kind of construction you want to make:
Proofreading of all outgoing quotes is a task which Mr Robert is responsible for.
Proofreading of all outgoing quotes, which Mr Robert is responsible for, needs to be done in a more timely way, going forward.
If the question has more to do with how to use the word routine, then I would suggest a separate question. Also, SE has a wonderful site for English Language Learners which you might want to try.