Will money be transferred alongside the character if I move from Xbox 360 to Xbox One

According to the information from Rockstar Support found here, You can transfer your progress to next generation consoles(Xbox one, PS4) and to a PC with the help of your Rockstar social club account. They have not mentioned about character transfer from PS3 to Xbox 360 in the provided link.

You can give it a try if you want with the procedure mentioned in their support link which I have given but, you will have only one chance and there are lot of limitations. Proceed at your own risk.

You can also post a question in Rockstar support for a definitive answer for your question.

No, you can not.

While you can transfer your character from Xbox 360 to Xbox One, you are making a copy of the character, and converting it to the newer console. From this point on, the Xbox One character is completely differant to the character on Xbox 360.

You also can not transfer your save back to the 360, as this feature was provided to allow players to upgrade consoles without worry about starting over, and does not support going in the opposite direction.