A BCI user awareness of an error is associated with a cortical signature named error-related potential (ErrP). The incorporation of ErrPs' detection in BCIs can improve BCIs' performance. This work is three-folded. First, we investigate if an ErrP classifier is transferable from able-bodied participants to participants with spinal cord injury (SCI). Second, we test this generic ErrP classifier with SCI and control participants, in an online experiment without offline calibration. Third, we investigate the morphology of ErrPs in both groups of participants. We used previously recorded electroencephalographic (EEG) data from able-bodied participants to train an ErrP classifier. We tested the classifier asynchronously, in an online experiment with 16 new participants: 8 participants with SCI and 8 able-bodied control participants. The experiment had no offline calibration and participants received feedback regarding the ErrPs' detection from its start. The generic classifier was not trained with the user's brain signals. Still, its performance was optimized during the online experiment with the use of personalized decision thresholds. Participants with SCI presented a non-homogenous ErrP morphology, and four of them did not present clear ErrP signals. The generic classifier performed above chance level in participants with clear ErrP signals, independently of the SCI (11 out of 16 participants). Three out of the five participants that obtained chance level results with the generic classifier would have not benefited from the use of a personalized classifier. This work shows the feasibility of transferring an ErrP classifier from able-bodied participants to participants with SCI, for asynchronous detection of ErrPs in an online experiment without offline calibration, which provided immediate feedback to the users.