Is it permissible to give the money vowed [for a mosque] to a different mosque than the one whose construction has been completed? And can the money be given in multiple installments?

Whoever vows obedience to Allah, it is obligatory for him to fulfill it, according to the hadith: "Whoever vows to obey Allah, let him obey Him." And spending money for the mosque is an act of obedience that must be fulfilled.

If the mosque is in need of the money, such as for operational expenses and the like, then it is obligatory to spend it on it. Otherwise, it is permissible to spend it on another mosque in need. It is also permissible to disburse the vowed amount in installments, unless it was specified to be paid in one lump sum.