płynący z głębi serca in inglese:

Please accept our heartfelt apologies.

My heartfelt condolences to your wife.

Sometimes books leave the impression that heartfelt desire and hard work alone will lead to improved performance.

Heartfelt thanks!

I would like to offer you my heartfelt thanks for this.

We all share the heartfelt wish that he and all the others will pass the admission examination.