Yes, you can reuse characters.
There is nothing special or special about Lost Phandelver Mines it requires different management of all other content. The characters are not implicit: you do not throw them out when you finish the book. Just because a lot of hardcover adventures are designed to start at L1, does not mean that they must do it.
Some modules even specifically indicate how to mix them. For example, The thunder of the king of storms has a section in the appendices that covers what to do with characters coming out of Lost Phandelver Mines. The short version is "skip chapter one and start with chapter two", but there are some more specific suggestions on how to incorporate it into a story. Other modules have different hooks or leave you the option of developing your own hooks.
Balancing being too high
If you start a hard cover adventure with characters higher than the recommended level, you will have to adapt to it (or at least be aware of it). Early encounters will certainly require that the opposition be corrected in one way or another, and even subsequent encounters may need it (the characters start too often, so they may be in danger). to be too late). This is where the discretion of the SM comes in.
It is also an opportunity to take into account the preferences of the players. Some players like danger at the edge of their seat and the risk of difficult or deadly encounters, as well as tactical thinking that can tip the odds in your favor to win. Other players prefer to enter a room and slaughter the enemies, scoring the score for each of them. As a DM, it's up to you to gauge your players and adjust matches accordingly.
One of the easiest ways to control the character's level is to not assign experience points, but to assign additional levels according to the needs of the story. This is known as important advancement. This can lighten the burden of a party too high, because you simply do not live up to meetings that are not really a challenge.