2 Timothy to  1 Corinthians

Grace for "all of us" and to "every place."

Grace to Everyone

22Our master Joshua the anointed be with your spirit. Grace be with all of us. Amen. 2 Timothy 4:22 (2 Timothy 4:22 BRB)
2To the assembly of god which is in Corinth FA , the called and holy who are holy by Joshua the anointed, and to all of them in every place who invoke the name of our master Joshua the anointed, both theirs and ours: 1 Corinthians 1:23Grace be to you and peace from god our father and from our master Joshua the anointed. 1 Corinthians 1:3 (1 Corinthians 1:2-3 BRB)

Second Timothy ends with Paul asking for grace for "all of us." The "us" is clearly Paul, Timothy and the list of people in the previous paragraph (who happen to be ministry workers). Basically Paul is extending grace to the larger ministry team.

Of Paul's many letters First Corinthians is unique because it's addressed to "everyone in every place" who invokes the name of Jesus. After addressing the letter to such a wide audience Paul extends grace to his readers as per his usual fashion. So grace is extended to a larger group then the core audience at both the end of Second Timothy and the beginning of First Corinthians.

Kept to the End

18My master will deliver me from every evil work and will give me life in his kingdom which is in the skies, for to him be glory forever and ever. Amen. (2 Timothy 4:18 BRB)
4I thank my god always on your behalf for the grace of god that has been given to you by Joshua the anointed, 5for in all things you are enriched by him in all utterance and in all knowledge 6because the testimony of the anointed has been confirmed in you. 7You do not lack any of his gifts, but wait for the revelation of our master Joshua the anointed 8who will also strengthen you to the end so that you may be blameless in the day of our master Joshua the anointed. 1 Corinthians 1:4-9 (1 Corinthians 1:4-8 BRB)

Paul is confident master will deliver him from various circumstances until his end, in the skies. Then he writes the Corinthians to say Jesus will strengthen them until the end, till the day of master.

Many Teachers

2Preach the word and stand by it zealously in time and out of time. Rebuke and reprimand through all patience of the spirit and teaching, 3for the time will come when men 1|4 will not obey sound teaching, 2|4 but they will add for themselves extra teachers, according to their desires, being lured by enticing words, 3|4 4and they will turn away their ears from the truth, 4|4 and they will turn to fables, 5but you 1|4 must be awake to all things, 2|4 and endure hardships, 3|4 and do the work of an evangelist, 4|4 and finish your ministry. (2 Timothy 4:2-5 BRB)
10I beg you my brothers in the name of our master Joshua the anointed to be of 1 accord and let there not be divisions among you but be perfectly united in 1 mind and in 1 thought. 11For I have been informed about you my brothers by the house of Chloe that there are disputes among you. 12This I say, because there are some among you who say, 1|4 I am a follower of Paul, and some who say, 2|4 I am a follower of Apollos, and some who say, 3|4 I am a follower of Peter, and some who say, 4|4 I am a follower of the anointed. 1 Corinthians 1:10-12 (1 Corinthians 1:10-12 BRB)

Another theme shared between Second Timothy and First Corinthians is that of having many teachers.