Is it permissible for me to shorten and combine prayers while traveling for work between cities in Germany for a period of three months, knowing that I will return to Lithuania thereafter?

If the stay in the country or city you traveled to is more than four days, then the concessions of travel, such as shortening prayers and breaking the fast, are not permissible for you. Rather, you are subject to the rulings for residents. As for the concessions of travel, they are only for the duration of the journey itself.