As far as I understand the original message the data has already been realigned and normalised within FSL, it seems to be more about the rp text file. There's nothing special about the rp file, it stores the necessary translations/rotations needed to reorient the images relative to the first volume of the series (or the mean volume depending on settings). If you have preprocessed your data with a different software you will receive a similar file, as realignment is really a fundamental step. There might be different conventions though, maybe the realignment parameters are e.g. based on a different origin, maybe it's not relative to the first or mean volume but always relative to the subsequent one. However, as long as all the subjects have been preprocessed the same way with the same package you don't have to worry about that. The obtained parameters stored in a certain format would be added during model specification (possibly the format has to be adjusted though).
But nonetheless you have to be careful when switching between different packages. As far as I remember when realigning 4D nii files (just estimate, no reslice) with SPM the realignment parameters are not stored in the header of the individual nii files (as there's just one big file) but in an extra mat file. These parameters are applied during the next module with a reslice step within your preprocessing pipeline, usually this would be the normalisation. If you switch between different packages and/or delete the mat file too early then relevant information would be lost, meaning although you ran realignment the parameters might actually not be applied on the data. To avoid this you should stay within a certain package for preprocessing purpose.