We have seen other examples of Tehreef in Musnad Imam Ahmad. You can read LINK 1, LINK 2, LINK 3. LINK 4 to get a examples of Tehreef in Musnad Ahmad. Anyways, let us see how this famous sunni imam does yet another tehreef

We find in Musnad Ahmad bin Hanbal

ثنا عبد الرزاق ثنا معمر عن الزهري عن مالك بن أوس بن الحدثان قال أرسل إلى عمر بن الخطاب رضي الله عنه فبينا أنا كذلك إذ جاءه مولاه يرفا فقال هذا عثمان و عبد الرحمن وسعد والزبير بن العوام قال ولا أدري أذكر طلحة أم لا يستأذنون عليك قال ائذن لهم ثم مكث ساعة ثم جاء فقال هذا العباس وعلي رضي الله عنهما يستأذنان عليك قال ائذن لهما فلما دخل العباس قال يا أمير المؤمنين اقض بيني وبين هذا وهما حينئذ يختصمان فيما أفاء الله على رسوله من أموال بني النضير فقال القوم اقض بينهما يا أمير المؤمنين وأرح كل واحد من صاحبه فقد طالت خصومتهما فقال عمر رضي الله عنه أنشدكم الله الذي باذنه تقوم السماوات والأرض أتعلمون ان رسول الله صلى الله عليه وسلم قال لا نورث ما تركنا صدقة قالوا قد قال ذلك وقال لهما مثل ذلك فقالا نعم قال فاني سأخبركم عن هذا الفئ ان الله عز وجل خص نبيه صلى الله عليه وسلم منه بشئ لم يعطه غيره فقال وما أفاء الله على رسوله منهم فما أوجفتم عليه من خيل ولا ركاب وكانت لرسول الله صلى الله عليه وسلم خاصة والله ما احتازها دونكم ولا استأثر بها عليكم لقد قسمها بينكم وبثها فيكم حتى بقي منها هذا المال فكان فكان ينفق على أهله منه سنة ثم يجعل ما بقي منه مجعل مال الله فلما قبض رسول الله صلى الله عليه وسلم قال أبو بكر رضي الله عنه أنا ولي رسول الله صلى الله عليه وسلم بعده أعمل فيها بما كان يعمل رسول الله صلى الله عليه وسلم فيها”

Malik bin Aus said that once Umar called me, and we were sitting when the Slave of Umar named Irfa came, and said that Uthman, abdur Rehman, Saad and Zubair wish to come in. He said: Call them in. Then he came back again and said that hazrat Ali and Abbas also wish to come in. He said: Let them come in.
When Abbass came, he said: Amir ul Momineen! Solve this issue between me and Him. At that time their main issue was in regards to property gained from bani Nadeer. People also said to solve this issue which is increasing
Umar said that I give u the promise from God by whom order Earth and Skies are there; do u people know that Allah’s Prophet said that We dont leave any property and what we leave, it is Sadaaqa/charity?
People agreed.
So he asked this from Abbass and Ali and they also agreed
Then he said let me inform you about this reality, Allah specified this with Prophet and he did not give anyone anything, this is specific to him only, but he did not save it for you nor gave it preference on you. He distributed it in you and when some was left, he gave that to his family for whole year.And even when that was left, he gave it in path of Allah. And when he died, abu Bakar said that he is the Wali of Prophet, and will act how Prophet asws acted.

[Musnad Ahmad, vol 1, page 259-260, narration 425]

Sheikh Shoaib terms this narration Sahih on the conditions of Sheikhain

[Musnad Ahmad, vol 1, page 482-483, narration 425, foot note 3]

Now, as it is clear that he took it from abdur Razaq, and he has included this narration in his Musanif; and there with the same sanad/chain of narrators, we find that the narration continues, and umar futher says

ثم أقبل على علي والعباس فقالوأنتما تزعمان أنه فيها ظالم فاجر والله يعلم أنه فيها صادق بار تالع للحق ثم وليتها بعد أبي بكر سنتين من إمارتي فعملت فيها بما عمل رسول الله صلى الله عليه و سلم وأبو بكر وأنتما تزعمان أني فيها ظالم فاجر

[Musnaif abd Razaq, vol 5, page 469-470, narration 9772]

online link

“Then he (Umar) turned to Ali and Abbas and said that you think that he (Abu Bakr) was unjust and immoral, but God knows that He was honest and follower of truth. And then I became Wali after abu Bakar’s rule of two years, and so I did what holy Prophet and abu Bakar did. And you think that I am unjust/zalim and fajir/immoral……………….”

so, We see that Ahmad bin Hanbal skipped those parts where the concept of Ali asws and Abbas was given regarding abu Bakar and Umar ……………………