this process is reversible and both form will occur in a relatively fast equilibrium. The position of the equilibrium vill depend on the ratio of pKa's, which can be estimated from literature data (this will be a reference your are looking for). The kinetic rates of the proton transfer would depend on many factors and in certain cases might be slow enough to study this process by NMR.
One last question, can proton transfer take place from water molecule to the studied compound. To be more clear, compound is surrounded by many clusters of water and forming two intermolecular H-bonds. So, these H-bonds are in equilibrium too as shown below N.....H-OH and NH...OH???!!! Compound pka=5.5
It do not happen, because water pKa is around 15 and your compound have a pKa of 5.5. Then, water never can act as an acid to protonate your compound. To do that, you need an stronger acid than your compound.