Supplication during and between the two prostrations

Also is the supplication, "Allahummagfirlee warhamni" by itself valid when sitting between the prostrations, because I have been saying this.
When sitting between the two prostrations i have been making the supplication "Rabbigfirlee warhamnee" once, just that and nothing extra on the end of it, thinking it was authentic. Now looking at the reported supplications for this position, I can only find this one but with extra on the end "...wajburnee, warfa'nee..." Does this mean that my prayers were invalid because I was not reading an authentic supplication? or can you read any supplication you like?

Walaikum assalam wa rahmatullah,

I pray that this finds you well, and in the best of health and spirits. May Allah grant you all good and success in this life and the next.

Any supplication would be fine there. Your past prayers are valid, Alhamdulillah.

The condition for valid supplication in prayer is that it either be (a) with something transmitted in the Qur'an and Sunna, or (b) something not resembling human speech--namely, something that one cannot ask other humans for. [ Ibn Abidin, Radd al-Muhtar; Shurunbulali, Maraqi al-Falah ] Thus, asking Allah that, "O Allah marry me to Zaid/Zubaida" within the ritual prayer would invalidate the prayer, as this is something one could ask another human for.

However, it isn't a condition that the supplication be specifically established in the Qur'an and Sunna. The reason for this is that the Divine Command, "Call upon Me, and I shall answer you," is general, and can be fulfilled. This was conditioned, when it comes to ritual prayer, by the words of the Messenger of Allah (peace and blessings be upon him), "No human speech befits this prayer of ours." [Related by Muslim, on the authority of Mu`awiya ibn al-Hakam (Allah be pleased with him), and others]

The legal rulings of supplication (du`a') in prayer:

(1) A confirmed sunna, in the final sitting before the final salams.

(2) Recommended, during prostration in supererogatory prayers.

(3) Good, during prostration in obligatory prayers for other than the imam.

(3) Good, to avoid the difference of opinion of those who deemed it necessary, between the two prostrations, by seeking forgiveness.

[ Ibn Abidin, Radd al-Muhtar ]

And Allah alone gives success.

Faraz Rabbani