Short answer. Yes. The rule expressly credits it. Where an accused has satisfied or served the earlier judgment in whole or in part, that service is credited in the event of conviction for the graver offense. The credit is built into the rule, not left to discretion.
What the law says
where the accused satisfies or serves in whole or in part the judgment, he shall be credited with the same in the event of conviction for the graver offense
Rule 117, Section 7 — Former conviction or acquittal; double jeopardy. Read the full provision →
The credit is written into the rule
The provision closes with a sentence aimed squarely at this problem. In any of the situations where a conviction does not bar a later prosecution for a graver offense, where the accused satisfies or serves in whole or in part the judgment, he shall be credited with the same in the event of conviction for the graver offense. The operative word is shall. It is not an equitable concession a court may extend or withhold; it is the consequence the rule attaches to the second conviction.
What counts as satisfying the judgment
The wording covers two things and covers them alike: an accused who serves the judgment and one who satisfies it. Imprisonment already undergone is the obvious case. But a judgment can also be satisfied by paying what it imposed, and the rule credits that as well, in whole or in part. You do not need to have completed the earlier sentence for the credit to operate — partial service is expressly included, which matters, because these situations usually arise while the first sentence is still running.
When the credit becomes relevant
The credit only comes into play if you are actually convicted of the graver offense. It does not shorten anything on its own, and it says nothing about whether the second prosecution was permissible to begin with. Those are separate questions, decided under the exceptions the same rule sets out — a graver offense that developed from supervening facts, facts constituting the graver charge discovered only after a plea was entered, or a plea of guilty to the lesser offense made without the required consent.
Making sure the credit is actually applied
Because the credit depends on facts outside the second case — how long you were detained, what you paid, when the first judgment took effect — it is worth having those records ready rather than assuming they will follow the case automatically. Commitment orders, official receipts and the entry of judgment in the earlier case are the ordinary proof. Raising the point at sentencing, with documents in hand, is far simpler than correcting a computation afterwards.