Spirit of Christ, spirit of God, Holy spirit are used interchagebly in the scriptures - to make a strict distinction between them is "futile" and unproductive.
We can see here that the prophetic "agent" is ascribed to both the spirit of Christ and the Holy spirit:
1 Pet 1:10 Of which salvation the prophets have inquired and searched diligently, who prophesied of the grace that should come unto you:
1 Pet 1:11 Searching what, or what manner of time the Spirit of Christ which was in them did signify, when it testified beforehand the sufferings of Christ, and the glory that should follow.
Acts 28:25 And when they agreed not among themselves, they departed, after that Paul had spoken one word, Well spake the Holy Ghost by Esaias the prophet unto our fathers,