The hadith was compiled on the authority of different sahabah:
- On the authority of ibn 'Abbas:
By ibn as-Sunni ابن السني in his 'Amal al-Yawm wal-Laylah عمل اليوم والليلة:
حدثني عبيد الله بن شبيب بن عبد الملك عن يزيد ابن سنان حدثنا عمرو بن الحصين حدثنا إبراهيم بن عبد الملك عن قتادة عن سعيد بن أبي الحسن عن ابن عباس رضي الله عنه قال قال رسول الله صلى الله عليه وسلم من قال إذا أصبح (اللهم إني أصبحت منك في نعمة وعافية وستر فأتمم علي نعمتك وعافيتك وسترك في الدنيا والآخرة) ثلاث مرات إذا أصبح وإذا أمسى كان حقا على الله عز وجل أن يتم عليه نعمته.
This narration is regarded as very weak as we have in the narrator chain Ibraheem ibn 'Abd al-Malik إبراهيم بن عبد الملك whom's level of trust is discussed, but all scholars agree that he used to forget or mix, further 'Amr ibn Hosayn عمرو بن الحصين is matrook (left) with a certain consensus as ibn Hajar said. This version was also compiled by al-Khila'i الخلعي in his Fawa'id as imam as-Suyuti quoted in his Da'iy al-Falahداعي الفلاح في اذكار المساء والصباح. AL-Albani qualified this hadith as fabricated.
- On the authority of abu Hurairah in ibn Hajar's Nata'ij al-Afkar نتائج الأفكار (Volume2 pages 412-413):
A side note: Ibn Hajar here not only displayed the hadith and commented it, but also shared the information when -exact day- he heard this hadith from his teacher.
This narration first of all only covers the first part of the hadith of ibn 'Abbas and further has some additions:
O Allah, I have reached the morning with blessings, strength a. So complete all the blessings and strength ... .
Here ibn Hajar was referring to the hadith of ibn 'Abbas and considered this narration as a kind of backup, as almost all narrators in the chain are of a high level of trust, even if the hadith as is compiled is unique in wording. Only -as you may read in the Arabic text- the narrator Habeeb ibn abi Habeeb حبيب بن أبي حبيب is considered as matrook and was also declared a liar by some scholars. Although he was known as the scribe of imam Malik.
As we see none of the versions of this hadith is safe from doubt.
My main source: This article -in Arabic- on alukah and islamweb fatwa #118932
When following a weak hadith is permissible
Basically one could follow a hadith which was declared as da'if in case of good deeds (sadqah, dhikr, du'a) under a number of conditions:
Al-Haafiz ibn Hajar (may Allaah have mercy on him) summed up the conditions for it to be permissible to act upon a saheeh hadeeth, which are as follows:
1 – It should not be very weak, and one should not act upon a hadeeth which was narrated only by one of the liars or those who are accused of lying, or whose mistakes are serious.
2 – It should mention a good deed for which there is a basis in sharee’ah.
3 – When acting upon it one should not believe that the action is well-founded, rather he should do it on the basis of erring on the side of caution. (Source islamqa #44877
Note that the wording of the hadith or dhikr by default doesn't sound bad at all. But based on the "worst case" scenario of the most negative qualifications one should avoid saying it and avoid inviting others to do so without adding a clear qualification that it is at least hardly or not authentic.