Answer

A difficult question. On the one hand, camaraderie is an important value, especially in the army. But at first glance it would seem that this is still forbidden, since it is assistance in a transgression, and even a case of "do not place a stumbling block" (because there is no one else who would replace him, making this a case of “the two sides of the river”). But there are quite a few grounds for leniency.
1. You are not assisting him in his act; you are only making it possible. He asks you to switch, and you agree. That in itself is entirely legitimate. What he decides to do is his business. Similarly, it was permitted to desecrate the Sabbath in order to save the life of a secular Jew, even though this is not a case of desecrating the Sabbath so that he will keep many future Sabbaths, since you are merely making it possible for him to keep Sabbaths, and what he actually decides to do is up to him.
2. Beyond that, if he does not believe at all, then in my opinion his transgressions are not transgressions, and there is no assistance or causing someone to stumble here.
3. Beyond that, leaves like this improve mood and morale and help the fighting effort.
4. Beyond that, he can desecrate the Sabbath in the army even if you do not replace him. Either way, he is not Sabbath-observant.
5. In addition, refusing in such a case involves desecration of God’s name, as the halakhic decisors wrote regarding the permission to serve refreshments to a secular guest when you know he will not recite a blessing.
6. And finally, if you do not agree to do this, it makes joint service of religious and secular soldiers in the army very difficult, which is itself problematic.
For all these reasons, bottom line, in my opinion this is permitted, and it is even proper to do so from the outset (because of the value of camaraderie).