If the one who is elected accepted and is an ordained bishop, the synod of bishops of the patriarchal Church proceeds with his proclamation and enthronement as patriarch according to the prescriptions of the liturgical books; if the one who is elected is not yet an ordained bishop, the enthronement cannot be performed validly before the one who is elected receives episcopal ordination.
1. By means of a synodal letter, the synod of bishops of the patriarchal Church notifies the Roman Pontiff as soon as possible
about the canonical conduct of the election and enthronement and that the new patriarch made a profession of faith and the promise
to exercise his office with fidelity in the presence of the synod according to the approved formulas. Synodal letters that an election took place are also to be sent to the patriarchs of the other Eastern Churches.
2. The new patriarch must as soon as possible request ecclesiastical communion from the Roman Pontiff by means of a letter signed in his own hand.
Some not so savvy readers might conclude from the canon you have quoted that your claim of equality for the Pope and the Patriarchs is real. It isn't.
No Eastern Catholic Patriarch presides over any Church with a higher ecclesiastical status than autonomous.
The Church of Rome is the only autocephalous Church in the Catholic Church. The Pope is not equal to the Patriarchs. He is their boss and superior.
This is clearly stated in the Canon Law of the Eastern Churcheshttp://www.intratext.com/IXT/ENG1199/_INDEX.HTM
The bishop of the Church of Rome, in whom resides the office
(munus) given in special way by the Lord to Peter, first of the
Apostles and to be transmitted to his successors, is head of the
college of bishops, the Vicar of Christ and Pastor of the entire
Church on earth; therefore, in virtue of his office (munus) he
enjoys supreme, full, immediate and universal ordinary power in
the Church which he can always freely exercise.
1. The Roman Pontiff, by virtue of his office (munus), not only
has power over the entire Church but also possesses a primacy of
ordinary power over all the eparchies and groupings of them by
which the proper, ordinary and immediate power which bishops
possess in the eparchy entrusted to their care is both strengthened and safeguarded.
2. The Roman Pontiff, in fulfilling the
office (munus) of the supreme pastor of the Church is always
united in communion with the other bishops and with the entire
Church; however, he has the right, according to the needs of the
Church, to determine the manner, either personal or collegial, of
exercising this function.
3. There is neither appeal nor recourse against a sentence or decree of the Roman Pontiff.
...and several other canons which repeat the superiority of the Pope over the Patriarchs.