Although trainer rights have been changed to allow
moodle/course:enrolconfig
moodle/cohort:config
moodle/cohort:view
trainers cannot enrol cohorts.
IIRC a trainer still can't do this even with these capabilities. I think if you create a new role in the category context and give that role those capabilities and then give that to the teacher it should work. I meant to document this but haven't so far, sorry. (But I will check if it hasn't been documented elsewhere)
Thank you Mary. However to me as a moodle admin greenhorn this sounds a bit complicated.