Is the husband committing a sin by helping someone register an apartment in the husband's name to avoid its use as a custody apartment for the wife and children, knowing that the wife has other apartments available for rent, and that this person claims the apartment is an investment and not a residence?

If registering the apartment in the husband's name is not an evasion of a due right or an avoidance of harm, then there is no sin upon the man or the husband in doing so. However, the matter should be documented and witnessed to preserve rights. As for providing housing for the children, the man has fulfilled his obligation. There is disagreement regarding the ruling on the residence of the custodial mother, and if a dispute arises, the Sharia court is the competent authority.