When Samsung Electronics became the world’s most profitable technology company last month, its de facto leader was in jail.

Lee Jae-yong, vice chairman and heir apparent to Samsung Group, faces charges that he bribed South Korean government officials to solidify his family’s control of one of the world’s biggest business empires. On Monday, prosecutors recommended that Mr. Lee should be sentenced to 12 years in prison.

Samsung, by contrast, appears to be doing just fine without its boss. The conglomerate’s electronics arm made $10 billion in profit last quarter, thanks in part to strong demand for its chips. Samsung has also begun to cast aside the cloud that fell over it last year when its Galaxy Note 7, a high-priced smartphone meant to challenge the Apple iPhone but which showed a proclivity to burst into flames, became one of the technology world’s most spectacular failures.

The question is how long Samsung can travel down both of these paths.

Should Mr. Lee go to prison, or if his reputation is too badly damaged, experts say it remains unclear whether the cadre of professional managers that reports to the Lees can make the strategic decisions needed to keep Samsung on the rise.