Oh, a converter wasn't included?!
Yes, the official website says this model "Includes 2 Black Fountain Pen Cartridges (8921)"

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I think that a converter will fit in a Cross pen if two cartridges fit inside, the spare one pointing in the opposite direction from the working one. If that is true for the Compact, then you must look to see whether the cartridge seat in the section has threads for the converter (the amber converter, 8030, for most fountain pen models) or not (the green converter, 8930, for the Townsend pen). The converters page on the official website does not mention the Compact pen

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(Just finding my manners) Thanks, vox, for your reply!