请给我 发票 tonation

I have a question regarding tonation. I've read somwhere that if more the 2 words with the 3rd tone are following each other then only the last is used with the 3rd tone, but all the foregoing ones are used with the 2nd tone. So that would mean that the following sentence till '我' '请给' are pronounced with the 2nd tone only '我' has already the 3rd one?

请给我 发票

Yes, exactly. When a 3rd tone is followed by another 3rd tone, it is pronounced as a 2nd tone.
e.g. 你好 “nǐ hǎo” would be like “ní hǎo”

But when we have three 3rd tone together, we do not change all of them, just change the one before last one.
e.g. 请给我 "qǐng gěi wǒ" would be changed to "qǐng géi wǒ".

If we have four 3rd tone together,
e.g. 请你给我 “qǐng nǐ gěi wǒ” would be changed to "qíng nǐ géi wǒ".