Why does Truck take time engaging into drive or reverse from park or from stop

What is your question?

Never had this problem until after accident. New transmission oil cooler. And transmission oil still has problem engaging into reverse or drive from park and also sometimes after. Should I have transmission filter and oil replaced? What is causing it to take time engaging into a drive gear or having to give little bit of gas to make it engage?

What makes this problem better or worse?

Happens all the time

How long has your 1998 Ford Ranger had this problem?

Since accident and trans cooler leaked almost all oil all over ground transmission was almost bone dry for 3 months. Replaced oil cooler and transmission oil and still has issue going into drive gear.