The sentence, "This module takes between 11 and 14 min. and is conducted by a trained examiner.", is correct. The phrase "11 to 14 min." cannot be used in this situation, even if the wording of the sentence is changed.
This module takes between 11 and 14 minutes and is conducted by a trained examiner. This module takes (anywhere) from 11 to 14 minutes and is conducted by a trained examiner.