EOF format is the native format of Embird Embroidery Software and it is fair to assume it is this software you have to use, to be be able to save in this unique format.
It is the main embroidery format used in stores all design objects, lettering and background image in a single file. It support numerous other embroidery design formats and can be used to repurpose them and convert to Embird's format.
We do not have information about any other software that supports saving to Embird's EOF format, so it might very well be possible that using the original software is the only way how to achieve emb to eof conversion.