[Aluback]

I would like to add this quote by one of their biggest scholars:

وبالجملة لا بد لنا من الاذعان بعدم كونهم عليهم السلام أنبياء وبأنهم أشرف وأفضل من غير نبينا (صلى الله عليه وآله وسلم) من الانبياء والاوصياء ولا نعرف جهة لعدم اتصافهم بالنبوة إلا رعاية جلالة خاتم الانبياء ، ولا يصل عقولنا إلى فرق بين بين النبوة والامامة ، وما دلت عليه الاخبار فقد عرفته ، والله تعالى يعلم حقائق أحوالهم صلوات الله عليهم أجمعين

On the whole, after admission of the fact that the Imams are not prophets, we are bound to acknowledge the fact that they are superior to all Prophets and Awsiya (legatees) except our Prophet (salutations and peace upon him and his family). To our knowledge there is no reason not to describe the Imams as Prophets except consideration to the status of the Final Prophet. Our intellect too, cannot perceive a distinction between Nabuwwah (prophethood) and Imamah.

Source: Bihar Al-Anwar by M.Baqir al-Majlisi, Volume 26, p.82