I need to correlate GHG emissions data (given in Gg CO2-equivalent or kt CO2-equivalent) with Climate Change Planetary boundary data (provided in t CO2) and put them into same unit.
1 G = 10^9 hence 1 Gg = 10^9 g = 10^6 kg = 10^3 t = 1000 t
For conversion of CO2eq to CO2, of course this can only be done if the gas in question is CO2 (in which case, 1 t CO2eq= 1 t CO2; since the global warming potential of CO2 is by definition 1).
However, if the gas in question is a non-co2 gas, you cannot convert it into CO2. For instance, the global emissions from livestock enteric fermentation are roughly 2.5 Gt CO2eq yr-1. However these are methane emissions, and this figure cannot be converted into CO2.
The conversion in this case can only be done from the original gas, say CH4 (or N2O in case of other non-CO2 gases) to CO2eq. Not the other way around.