Full procedure ILS RWY 27 in India. We were about 4 miles from turning inbound. ATC cleared us the ILS APP and used the words "report established."
NOT "report established ILS" Or "report established LOC". Just "report established"
Say "BIGJET123 established on LOC". If local ATCO needs you to be established on the glide, he'll let you know then.
From my experience, ATCO just needs to know if the pilot has resumed navigation and can follow the ILS (or whatever approach it is) on his own. So reporting localiser only is fine enough. Of course the only and real purpose of these reports is for ATC not forgetting the transfer to TWR.