What is the solution for a husband who is negligent in performing prayers on time, despite knowing their importance?

Wasting the prayer is one of the greatest major sins. Missing even one prayer beyond its prescribed time is a greater sin than adultery, theft, drinking alcohol, and murder, by consensus. Your husband is in grave danger if he leaves the prayer out of laziness until its time expires, as this is a great major sin considered disbelief by some scholars. Continue to advise him and let him listen to lectures and fatwas that warn against abandoning prayer. If he persists in this and you despair of his response, then there is no good for you in remaining with him.