When were the apostles baptised?

Dear Catholic Answers Apologist,

When were the apostles baptised?
Did they baptise each other after Jesus’ ascension? (having received the great commission, Mt 28)
If not, when?
And if not by each other - by whom? Our Lord?

Sacred Scripture does not give us an answer as to when and how the Apostles were baptized (other than St. Paul in Acts 9:18). However, we should remember what a sacrament is:

Question: What is a Sacrament?

Answer: A Sacrament is an outward sign instituted by Christ to give grace.

The essence of a sacrament is to receive grace. Just as the Apostles received confirmation through fire and not chrism, Christ could have chosen an alternate means of imparting the grace of baptism to them.

There is a tradition that the Apostles did receive water baptism. The Byzantine monk John Moschus wrote down the tradition:

Yes, truly, the apostles were baptised, as Clement the Stromatist relates in the fifth book of the Hypotyposes. For, in explaining the apostolic statement, “I thank God that I baptised none of you,” he says, Christ is said to have baptised Peter alone, and Peter Andrew, and Andrew John, and they James and the rest.

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