Can You Pray Duha If You Missed Fajr?
Question

One of the sisters told me that if a person did not pray Fajr on time, i.e., he prayed it after sunrise, he cannot offer the Sunnah prayer of Duha, i.e., no one can offer the Sunnah prayer of Duha who did not offer (Fajr) prayer on time. Is this correct?
Praise be to Allah.Is Duha prayer Sunnah?
Duha prayer is a confirmed Sunnah; it is proven that the Prophet (peace and blessings of Allah be upon him) did it, as Muslim (1176) narrated from `Aishah (may Allah be pleased with her) that she said: The Messenger of Allah (blessings and peace of Allah be upon him) used to pray Duha with four Rak`ahs, and more as Allah willed. 
An-Nawawi (may Allah have mercy on him) said: “Our companions said: Duha prayer is a confirmed Sunnah .” (Al-Majmu`, 3/528) 
Shaykh Ibn Baz (may Allah have mercy on him) said in Majmu` Al-Fatawa (11/389): “Duha prayer is a confirmed Sunnah that the Prophet (blessings and peace of Allah be upon him) did and taught his companions to do.”
Is it permissible to pray Duha if you miss Fajr?
If a person missed Fajr prayer, but made it up after sunrise, then he may pray Duha , because Duha prayer is a confirmed Sunnah that has no connection to Fajr prayer, and has nothing to do with the time of Fajr prayer at all, or whether it was done on time or made up later. 
Rather what is prescribed for one who has fallen short in some deed, or missed out on something good, is to do a lot of good and righteous deeds, the best of which are the Nafl (supererogatory) prayers . 
Rabi‘ah ibn Ka‘b Al-Aslami (may Allah be pleased with him) said: I used to stay overnight with the Messenger of Allah (blessings and peace of Allah be upon him) and bring him water for Wudu and whatever he needed. He said to me: “Ask.” I said: I ask to be with you in Paradise. He said: “Is there anything else?” I said: That is all, He said: “Help me to do that for you by prostrating a great deal.” (Narrated by Muslim, 489) 
An-Nawawi (may Allah have mercy on him) said: “This indicates that it is encouraged to prostrate a great deal; what is meant is prostration in prayer.” (Sharh Muslim) 
Ma‘dan ibn Abu Talhah (may Allah have mercy on him) said: “I met Thawban, the freed slave of the Messenger of Allah (blessings and peace of Allah be upon him), and said: Tell me of a deed that I may do, by which Allah may admit me to Paradise – or he said: Tell me of the most beloved of deeds to Allah. He remained silent. I asked him (again) and he remained silent. I asked him a third time and he said: I asked the Messenger of Allah (blessings and peace of Allah be upon him) about that and he said: “You should prostrate to Allah a great deal, for you will not perform one prostration to Allah but Allah will raise you one degree in status thereby and erase one sin for you.”” (Narrated by Muslim, 488) 
And Allah knows best.