You will find many ahadith without the addition "prays two raka'at" where it's said that anybody who made a proper wudu and prayed Allah will grant him whatever he may pray for, sooner or later or at least between the prayers he did with such a wudu.
Here 4 Examples of ahadith which are very similar to the narration you quoted from Imam Ahmad:
Authenticity of the Hadith
Now shortly to the Hadith you mentioned was quoted in Musnad al-Imam Ahmad and describes that abu a-Darda' wanted to leave some words of the Prophet (Peace be upon him) to the people when he felt that he will die and it's narrated by the young sahabi Yousouf ibn 'Abdullah ibn Salam who used to accompany abu a-Darda' (May Allah be pleased with both of them), afterwards abu a-Darda' added an advice (avoiding to turn left or right during prayer especially in fard):
حَدَّثَنَا مُحَمَّدُ بْنُ بَكْرٍ , قَالَ : حَدَّثَنَا مَيْمُونٌ يَعْنِي أَبَا مُحَمَّدٍ الْمَرَئِيَّ التَّمِيمِيَّ , قَالَ : حَدَّثَنَا يَحْيَى بْنُ أَبِي كَثِيرٍ , عَنْ يُوسُفَ بْنِ عَبْدِ اللَّهِ بْنِ سَلَامٍ , قَالَ : صَحِبْتُ أَبَا الدَّرْدَاءِ , أَتَعَلَّمُ مِنْهُ , فَلَمَّا حَضَرَهُ الْمَوْتُ قَالَ : آذِنْ النَّاسَ بِمَوْتِي , فَآذَنْتُ النَّاسَ بِمَوْتِهِ , فَجِئْتُ وَقَدْ مُلِئَ الدَّارُ وَمَا سِوَاهُ , قَالَ : فَقُلْتُ : قَدْ آذَنْتُ النَّاسَ بِمَوْتِكَ , وَقَدْ مُلِئَ الدَّارُ وَمَا سِوَاهُ , قَالَ : أَخْرِجُونِي , فَأَخْرَجْنَاهُ , قَالَ : أَجْلِسُونِي , قَالَ : فَأَجْلَسْنَاهُ , قَالَ : يَا أَيُّهَا النَّاسُ , إِنِّي سَمِعْتُ رَسُولَ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ , يَقُولُ :
" مَنْ تَوَضَّأَ , فَأَسْبَغَ الْوُضُوءَ , ثُمَّ صَلَّى رَكْعَتَيْنِ يُتِمُّهُمَا , أَعْطَاهُ اللَّهُ مَا سَأَلَ مُعَجِّلًا أَوْ مُؤَخِّرًا"
He who makes Wudu, and does it properly, then prays two rak'at, Allah will grant him whatever he may pray for, sooner or later.
, قَالَ أَبُو الدَّرْدَاءِ : يَا أَيُّهَا النَّاسُ , إِيَّاكُمْ وَالِالْتِفَاتَ , فَإِنَّهُ لَا صَلَاةَ لِلْمُلْتَفِتِ , فَإِنْ غُلِبْتُمْ فِي التَّطَوُّعِ , فَلَا تُغْلَبُنَّ فِي الْفَرِيضَةِ .
and by a-Daraqutni who qualified it's isnad as hassan and there's another version also quoted by Imam Ahmad and at-Tabarani amd Ibn abi 'Assim (in his book al ahaad wal matani) via Ibn Abi Sahl, from Kathir ibn Yassar and Yousouf ibn abdullah ibn Salam where the narrator (Sahl) wasen't sure whether abu A-Darda' said 2 or 4 rak'a!
The weakest Rawy of the chain of the Hadith you mentioned is Yahya ibn Kathir يَحْيَى بْنُ أَبِي كَثِيرٍ who was known to be mudalis and to make irsal ("jumping" the narrator chain).
About Muhamad ibn Bakr al-Bursani al Basri مُحَمَّدُ بْنُ بَكْرٍ i found him qulaified as trustworthy by ibn Ma'yn and Imam Ahmad and both Imam al-Bukhari and Muslim have quoted ahadith narrated by him. But it seems he wasn't known for being a famous Muhadith of his time, so he has only few ahadith!
Maymoun (Abu Muhammad al-Murni a-Tamimi مَيْمُونٌ (أَبَو مُحَمَّدٍ الْمَرَئِيَّ التَّمِيمِيَّ was qualified to be unknown, this could be an other weak rawy of this chain!
While Yousouf ibn Abdullah ibn Salam is a sahabi يُوسُفَ بْنِ عَبْدِ اللَّهِ بْنِ سَلَامٍ (who have been a child when the Messenger of Allah (peace be upon him) died).
So this hadith can't reach by any means any of the Versions without this addition of "prays two raka'at" which i quoted in the first part of my post.
And Allah knows best