"Perfect communion" refers to a state of strong and harmonious connection or understanding between two or more people, where they share ideas, feelings, or thoughts effortlessly, without any obstacles or misunderstandings. Full definition
«Like angels» simply means in perfect communion with God. (religion-online.org)
Using the definition of the declaration, which is the definition enshrined in the historic documents of the Catholic Church, the ODF recognizes that there are churches in the proper theological sense, that have both authentic bishops and an authentic Eucharist, but are not in perfect communion with the Catholic Church. (religion-online.org)
It is our hope and prayer as Evangelicals and Catholics that by rightly using the means of grace afforded to us in the Church here on earth, we will be more fully conformed to Christ and thus be drawn into more perfect communion with one another and with the communio sanctorum triumphant, to the glory of the one and immortal God, the Father, the Son, and the Holy Spirit. (firstthings.com)