The opposite is true:

EEG = GainMatrix x Source

This is the so called 'forward problem'. To solve the 'inverse problem' you need to invert the gain matrix and when there are more sources than channels, pseudo-inverse with regularisation is necessary. Different ways to regularise correspond to different assumptions about the source covariance matrix and these map to different inverse methods such as 'minimum norm', 'LORETA', 'MSP' etc. So you can easily use the gain matrix in SPM to simulate data but there is a reason inverse solutions require more work.

Best,

Vladimir