Custom Widjet for import news from one site to another

i want a custom widget so i can import news from one site to another. for example: i have the website [login to view URL] with i am updating daily with news in 4 different categories. when i am updating this website then i want automatically the new context (not all of it - just a selction) to go automatically on the other site that i have with the name www.tsakbet.gr. i am willing to pay maximum 55 USD. for more information por to have an idea please check the website [login to view URL] and take a look on the first widhet on your left with the name SPORT24 NEWS. inside that widget i like to have the context of my [login to view URL]