With the caveat that recon would be an even better indicator, the eye of Henri looks pretty good as it begins to cross into the Gulf Stream. It looks circular with convection (albeit weak) wrapping around it. You can also see fast low level motion that may be indicative of a tighter and stronger wind field.
Of course, we don't know if winds are mixing down or if the pressure is dropping, but it looks good. If crossing the GS can pop some hot towers and evacuate some of the residual dry air, it could quickly improve in presentation and organization in the few hours before reaching cooler waters.