What is the ruling of the Sharia on how to fulfill a vow to donate two sacrificial animals every year, given that the original wording of the vow is not remembered, and there is a difference in the value of the sacrificial animal and the place of its slaughter depending on whether one is in the home country or Europe?

The default is that a vow (nadhr) does not occur, and fulfilling something one doubts about is not obligatory unless its conditions and pillars, including verbalization, are confirmed. So, whoever doubts whether he verbalized a vow is not obliged to fulfill it, as the default is non-existence. However, if you fulfill it as a precaution for your faith, that would be more appropriate. Whoever vows an act of proximity (qurbah) must fulfill it according to its description. So, whoever vows to offer a sacrifice (udhiyah) is not permitted to give its monetary value, but it is permissible for him to appoint someone to buy the sacrificial animal and slaughter it.