The G3P is converted to 1,3-bisphosphoglycerate in the presence of enzyme glyceraldehyde-3-phosphate dehydrogenase (an oxido-reductase).
The aldehyde groups of the triose sugars are oxidised, and inorganic phosphate is added to them, forming 1,3-bisphosphoglycerate.
The hydrogen is used to reduce two molecules of NAD, a hydrogen carrier, to give NADH + H for each triose.
Hydrogen atom balance and charge balance are both maintained because the phosphate (P) group actually exists in the form of a hydrogen phosphate anion (HPO), which dissociates to contribute the extra H ion and gives a net charge of -3 on both sides.