@Exbrit said:

@Paradisefound said:
Please come home Mango ❤️

Suggestion: make some flyers with Mango’s photo on them. Offer a reward. If you have a radio station mention it to them. These types of birds stand out and many times people will hear a different sounding bird and take notice.

I’ve recovered parrots that flew up to ten miles away. It’ll take some time (days), but hopefully someone will give you a lead.

Some years ago a small beautiful parrot showed up at my sister’s bird feeding stations, after a big storm the night before. It stayed there for about a week, pretty much moving onto their patio. Sure enough though, someone was going door to door asking if anyone has seen xbird, my sister said yep, he’s out back, help yourself!

From the net.

Lovebirds fly away, but they don’t do so because they are desperate to escape your care.

Do lovebirds come back if they fly away?

They will certainly do their best to do so.
However, lovebirds do not have the strongest sense of navigation, and it’s important for you to realize that your bird has never seen your home from the air.
It doesn’t know what to look for.
That said, its natural instinct will be to fly home if it can find its way. often, lost birds will just come back of their own accord, to where they have comfort, shelter, food and water.
Try placing their favorite or most colorful toys outside to draw their attention.

Whenever possible, bring the cage to the bird. For a missing bird, place the cage near the site of the fly-away. If your bird flies out through your front door, for example, place the cage on your porch or doorstep. Whenever possible, hang the cage outside so that it appears just as it would indoors.

Add large amounts of your bird's favorite foods and tasty treats in or around the cage to lure the bird back home. Someone should always be at the ready near the cage to pounce with a towel or net. Use large pieces of food that are easily visible, and leave the cage with the door open.

If you are unable to lure a missing bird back home with cage and food, try "calling" it by name and simply remain in the area, repeating familiar words, sounds, and phrases. In some instances, this may entice your pet to fly down to you.
If you regularly play music of a certain type, play some quietly outside. Make it easy for the bird to locate where the sound is originating as a familiar beacon.

Neighborhood kids may love searching for birds, especially if a reward is offered.

Edited to add:
Your roof is often a common spot for pet birds, especially if they tried to get back into your house. Most birds won’t be able to re-locate the window or door, so they may end up on the roof. All trees and structures should be scanned 360 degrees around. Even if your bird is brightly colored, it is relatively easy for them to hide behind leaves.

The owner of the bird should stay outside and preferably wear bright clothing. A bird does not know what their house looks like and has no way to identify it from the air. Even if they want to get home, they likely won’t be able to find it.
The one familiar landmark that you can provide for your bird is you. Therefore, it is crucial to ensure that you are outside as much as possible. If your bird happens to fly over your house, they may see you and return on their own accord. Many captive birds will fly back to their owners if they find them. Many don’t want to remain in the unknown and scary outside.
But your bird can’t find you if you’re in the house.