Ex-Dolphins Player -- Dramatic 1st Video ... Moments After 9-Mile Swim

Here is the dramatic first video of ex-Miami Dolphins player Rob Konrad -- shot moments after he made contact with police ... following a fishing boat accident which forced him to swim 9 death-defying miles to shore.

The footage -- shot from multiple cameras inside a police cruiser -- was shot around 5AM on January 8th in Palm Beach, FL ... after Konrad fell off his fishing boat and spent the next 16 hours swimming for his life.

When Konrad reached land, he rang the doorbell of an oceanfront home ... and cops responded immediately.

The cops were very accommodating -- grabbing blankets, water and helping Konrad make calls to loved ones so they knew he was OK.

Konrad was later hospitalized for dehydration and hypothermia ... but was eventually released.

During a news conference the following week, Konrad said he kept thinking about his family during the swim ... and that's what gave him the strength to keep going.