Which shoulder ligament runs from the fingerlike projection of the coracoid process (superior to the glenoid cavity) to the collarbone?

It is the coracoclavicular ligament. As the name indicates it connects the coracoid process to the clavicle (collarbone). This ligament is made of two parts, the trapezoid ligament and the conoid ligament. These ligaments impede opposite movements of the scapula in relation to the clavicle.