There is a better chain for this hadith which has been classed as Sahih by scholars including Nawawi, Ibn Khuzaimah, Ibn Hibban, Hakim and Dahabi, al-Albani and others.
There is also a hint about it in the Quran:
فلما قضينا عليه الموت ما دلهم على موته إلا دابة الأرض تأكل منسأته فلما خر تبينت الجن أن لو كانوا يعلمون الغيب ما لبثوا في العذاب المهين
And when We decreed for Solomon death, nothing indicated to the jinn his death except a creature of the earth eating his staff. But when he fell, it became clear to the jinn that if they had known the unseen, they would not have remained in humiliating punishment.
— Quran 34:14
Which implies that body of Solomon عليه السلام did not decompose after his death, as the only sign of death that the Jinn observed was that he fell when termites had eaten the staff on which he was leaning.
And there are other sahih reports which corroborate or support its meaning, such as:
مررت على موسى وهو يصلي في قبره
I passed by Moses when he was praying in his grave