The U2 frontman is great friends with former Oasis guitarist Noel and introduced the 19-year-old musician to the Manchester group's music a couple of years ago, and Bono has now managed to get Elijah and his bandmates a slot opening for Noel Gallagher's High Flying Birds this summer.
The 'Wonderwall' hitmaker was clearly impressed by Inhaler, who he has described as ''early U2''.
Noel told BBC Radio 2: ''Hi's son's got something.
''Eli has been getting it together for a few years and has gone through the stages most young people do.
''He started off a bit like The Clash, a bit angry.
''They're going to do some gigs with me in the summer.
''They're a bit like the [Echo and the] Bunnymen and early U2, which is a surprise.''
Noel and Bono - who also has two daughters, Jordan, 30, and Eve, 27, and John, 17, with wife Ali Hewson - often goes on holidays together and the Irish music icon is always texting the Britpop legend bizarre things he doesn't understand.
The 'Black Star Dancing' singer added: ''He sends me texts all the time.
''I show them to Sara [his wife] and go, 'What do you think he means by that?; and then I just ignore him.''
As well as Elijah, Noel's 19-year-old daughter Anais Gallagher - who has snapped several photos of Inhaler and worked on their artwork - is set to join her dad on tour in Japan to get some experience under her belt after starting a course in photography.
However, Noel says he's warned his daughter that she won't be getting much time to be a tourist and go shopping as he wants her to learn ''the brutality'' of his work.
He said: ''She's doing a photography course at uni and she's coming on tour with me.
''We're going to Japan. It will be good for her to see the brutality of my regime.
''I was like, 'You're going but there's no such things as days off.'
''She was like, 'What about shopping?'
''I went, 'You won't be doing any.'''
Noel recently joked that his children are ''lucky bastards'' to have him as a dad as he performed at the London Palladium last week.
The 51-year-old rocker played an intimate gig at the historic venue and among the 2,300 fans in attendance were his wife Sara MacDonald and their two sons, Donovan, 11, and Sonny, eight, and Anais - whose mother is his ex-wife Meg Mathews.
Showcasing his sarcastic humour, Noel dedicated his High Flying Birds hit 'AKA... What A Life!' to his three kids by saying: ''I'd like to dedicate this song to my three kids who are here. You lucky bastards. You lucky, lucky bastards.''
His new album Underneath It All is out now.
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