Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, thanks for your question, which emanates from a God-fearing heart, since it shows your commitment to da`wah, the basic duty of every Muslim. We’d would like to commend your pursuit of Islamic counseling.
As for your question, Muslims should be kind and gentle when dealing with all people, including non-Muslims, so that they will have the chance to see the true Islam through their practical good behavior. Therefore, if a non-Muslim, out of respect for Muslims or in order to learn Islamic prayer, joins them in salah, he/she is allowed to do so.
Responding to your question, Dr. Muzammil H. Siddiqi, former President of the Islamic Society of North America, states:
Muslims must pray with wudu’, but if a non-Muslim, out of respect for Muslims or in order to learn Islamic prayer, joins them in Prayer, he/she is allowed to do so. This may be a way for this person to come closer to Islam, and Allah may lead him/her to the right path.
Also, as a rule we should know that if a Muslim prays without wudu’, his/her prayer is not valid, but it does not invalidate the prayers of those who are standing in the same line with him/her.
Almighty Allah knows best.