As we consider the different aspects of “inheritance”, you may want to refer to the previous post, which treats the etymological and cultural considerations in more detail.
The word least frequently used in New Testament writings is prototokos, “firstborn”, which appears only 9 x. Except for Heb.11:28, where the writer recounts the Passover experience in Egypt, the word is exclusively applied to the Lord Jesus himself. It is used twice in the infancy narratives (Mt.1:25, Lk.2:7), relating physically to Mary, but all the rest are clear statements of Jesus’ primacy. Paul acknowledges him as “the firstborn among many brothers” (Rom.8:29), the one to whom we are all destined to be conformed; “the firstborn of all creation” (Col.1:15), the one who created and sustains all the rest; and “the firstborn from the dead” (Col.1:18), by his glorious resurrection demonstrating his position to be of the absolute highest rank. A similar thought accompanies the reference in Heb.1:6 to his “introduction” to the world by the Father. The joyful consummation is likewise celebrated in Heb.12:23 and Rev.1:5. Remember (and give thanks!) that the Firstborn, besides being the deserving recipient of all glory, power and praise, has accepted responsibility for the welfare of all the rest of the family!
Only a little more frequent is the term kleros, translated 8 x as “lot” (Mt.27:35, Mk.15:24, Lk.23:34, Jn.19:24) in the scene at the cross, Ac.1:21 regarding Matthias ( and also 3x in 1:17 and 1:25, where “part” is used, as it is in Ac.8:21 of Peter’s rebuke to the conniving Simon). Only in I Pet.5:3 is it translated “heritage”, where the church is called “God’s heritage.”
Diatheke, as noted in the previous post, presents a problem, in being translated half the time as “covenant” and half as “testament”, which, Heb.9 explains, is a reference to a legal will. Inheritance by will differs from familial inheritance in that blood relationship is not required, although (see previous posting) under Roman law, citizenship was required. As citizens of his Kingdom, and members of his family, of course, Jesus’ people qualify on both counts!
Many of the passages where diatheke appears, clearly reference the historic “covenants” (Lk.1:72, Ac.3:25, 7:8; Rom.9:4, 11:27; Gal.4:24, Eph.2:12, II Cor.3:14, Heb.8:9, 9:4, 9:15; Rev.11:19.)
Four refer to the prescribed legal technicalities required in any “covenant” or “will” (Gal.3:15,17; Heb.9:16,17.)
Most significantly, however, the letter to the Hebrews details two elaborations upon Jesus’ announcement (Mt.26:28, Mk.14:24, Lk.22:20), which Paul quoted in ICor.11:25, of a “new covenant / testament / will”, explaining the inadequacy and failure of the old (Heb.8:9, 10; 9:15) – also seen in II Cor.3:14 – and describing Jesus’ establishing of a “new” (Heb.9:15) and “better” (Heb.7:22, 8:6) one, “not like the old” (Heb.8:9). Identifying Jesus as the fulfillment of ancient prophecies, stating that God had always intended to remedy the weakness and failure of the former “covenants” (Heb.8 and 9), the writer details their failings. Unfortunately, many interpreters have used distorted fragments of this passage to identify the death of Jesus with the ancient ritual sacrifices – which are here declared to be an exercise in futility – completely ignoring the fact that it had already been established (Heb.2:14,15) that the real purpose and effect of that event, because he emerged triumphant on the other side of the grave, was to destroy death itself! The later references (Heb.10:15-17, 12:24; 13:20) emphasize that triumph, and (10:29) the glorious accomplishment of setting aside the faithful as God’s own possession. We are strictly warned not to depreciate this accomplishment!
More dominant than all of these other words combined are kleronomeo (v),”to inherit”, kleronomia (n), “inheritance”, and kleronomos , “heir”. Four times in the synoptics, in parable (Mt.21:38, Mk.12:7, Lk.20:14) and personal encounter (Lk.12:13), the term applies strictly to legal, temporal inheritance, and five times (Ac.7:5, Rom.4:13,14; Gal.4:30, Heb.11:8) to God’s promise to Abraham. In Gal.4:1, Paul refers to the legal requirement of majority (age) for inheritance. A formal declaration by the father was necessary to establish his son as an heir, when he attained legal age. Might this be the prototype of the “voice from heaven” recorded at Jesus’ baptism and again in the transfiguration accounts?
Jesus’ own inheritance, already discussed above as the Firstborn, is also noted in Eph.1:18 – as consisting of his people! – and Heb.1:2 and 1:4, as his being “heir of everything” and his consequent supremacy over all created beings.
All the rest (at least 30 references) refer to the heritage of the Lord’s faithful people!
Of special interest is the invitation to those among “the nations / Gentiles” (Mt.25:34), W.S.#62, to “inherit the kingdom prepared for you all from the foundation of the world!” This is an unmistakable reaffirmation that the intention was always the inclusion of all who would choose faithfulness.
“The Kingdom” (W.S.#19,20,21) is identified with inheritance in I Cor.15:50, Gal.5:21, Eph.5:5, Jas.2:5, and “the promise” in Gal.3:29, Heb.6:12, 6:17, 9:15. “The promise” is also related in Mt.19:29, and in discussions with several of Jesus’ questioners (Mk.10:17, Lk.8:18,10:25) to “eternal life” (W.S.#28).
Remember: one does not receive an inheritance after HE dies, but as explained in Heb.9:15-16, after the death of the person who wrote the will!
Thus Paul writes to the folks at Ephesus in the aorist tense – the inheritance has already been conferred (Eph.1:11), and to the Romans (8:17) and Galatians (4:7) in the present tense – “we are heirs!”
To be sure, there is more to come – Col.3:24 looks forward to the eventual receipt of “the reward of the inheritance” and I Pet.1:4 to the bestowal of the “inheritance that cannot decay, or be polluted, or fade away”, already secured by the Lord Jesus, but presently “kept in heaven”.
Paul (Eph.1:14) considers the Holy Spirit’s presence and power among us as merely a “down-payment” or guarantee of all that awaits the final consummation, when , with Jesus himself, those who remain faithful (Rev.21:7) “shall inherit all things”, and (Heb.1:14) also finally “inherit salvation”! (W.S.#5)
“Dear people, NOW we are God’s children (tekna): and it hasn’t been revealed yet what we will be! But we do know that when he [it] is revealed, we will be like him – for we shall see him as he is!” (I Jn.3:2)
Thanks be to God!
The Pioneers' New Testament 
Thanks, Ruth, for your continuing contribution to my understanding of The Word. May God continue to bless your efforts.